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8th Grade Scientific Notation
2015shy11shy20
wwwnjctlorg
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Table of ContentsClick on the topic to go to that section
bull Purpose of Scientific Notation
bull Magnitude
bull Glossary
bull Writing Numbers in Scientific Notation
bull Converting Between Scientific Notation and Standard Form
bull Comparing Numbers in Scientific Notation
bull Multiply and Divide with Scientific Notation
bull Addition and Subtraction with Scientific Notation
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
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Purpose ofScientific Notation
Return to Table of Contents
5
Purpose of Scientific Notation
Scientists are often confronted with numbers that look like this300000000000000000000000000000000000000000000000000000 kgCan you guess what weighs this much
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Blue Whale shy largest animal on earth
The Great Pyramid at Giza
Total Human Population
The Earth
The Sun
2000000000000000000000000000000 kg
60000000000000000000000000 kg
300000000000 kg
600000000 kg
180000 kg
Can you match theseBIG objects to their weights
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Click object to revealanswer
60000000000000000000000000 kg
2000000000000000000000000000000 kg 300000000000 kg
600000000 kg
180000 kg
Blue Whale shy largest animal on earth
The Great Pyramid at Giza
Total Human Population
The Earth
The Sun
300000000000 kg
Can you match theseBIG objects to their weights
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grain of sand
steam000000000035 kg
000015 kg
0000000000000000000000000030 kg
molecule
Can you match these small objects to their weights
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000000000035 kg
000015 kg
Click to reveal the answers
0000000000000000000000000030 kg
grain of sand
steam
molecule
10
The examples were written in standard form the form we normally use But the standard form is difficult to work with when a number is HUGE or tiny if it has a lot of zeros
Scientists have come up with a more convenient method to write very LARGE and very small numbers
Scientific Notation
Writing numbers in scientific notation doesnt change the value of the number
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Scientific Notation uses Powers of 10 to write big or small numbers more conveniently
Scientific Notation
Using scientific notation requires us to use the rules of exponents we learned earlier While we developed those rules for all bases scientific notation only uses base 10
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Powers of Ten
Click here to see a video on powers of ten which puts our universe into perspective
Click here to move from the Milky Way through space towards Earth to anoak tree and then within a cell
101 = 10
102 = 10 x 10 = 100
103 = 10 x 10 x 10 = 1000
104 = 10 x 10 x 10 x 10 = 10000
105 = 10 x 10 x 10 x 10 x 10 = 100000
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Powers of Integers
Powers are a quick way to write repeated multiplication just as multiplication was a quick way to write repeated addition
These are all equivalent
103(10)(10)(10)
1000
In this case the base is 10 and the exponent is 3
14
Review of Exponent RulesRemember that when multiplying numbers with exponents if the bases are the same you write the base and add the exponents
25 x 26 = 2(5+6) = 211
33 x 37 = 3(3+7) = 310
108 x 10shy3 = 10(8+shy3) = 105
47 x 4shy7 = 4(7+shy7) = 40 = 1
15
1 102 x 104 =
A 106
B 108
C 1010
D 1012
Answer
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2 1014 x 10shy6 =
A 106
B 108
C 1010
D 1012
Answer
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3 10shy4 x 10shy6 =
A 10shy6
B 10shy8
C 10shy10
D 10shy12
Answer
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4 104 x 106 =
A 106
B 108
C 1010
D 1012
Answer
19
Writing Numbers in Scientific Notation
Return to Table of Contents
20
Scientific Notation
Here are some different ways of writing 6500
6500 = 65 thousand65 thousand = 65 x 100065 x 1000 = 65 x 103
which means that 6500 = 65 x 103
6500 is standard form of the numberand 65 x 103 is scientific notation
These are two ways of writing the same number
21
Scientific Notation
65 x 103 isnt a lot more convenient than 6500
But lets do the same thing with 7400000000which is equal to 74 billionwhich is 74 x 1000000000which is 74 x 109
Besides being shorter than 7400000000 it is a lot easier to keep track of the zeros in scientific notation
And well see that the math gets a lot easier as well
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Scientific Notation
Scientific notation expresses numbers as the product of
a coefficient and 10 raised to some power378 x 106
The coefficient is always greater than or equal to one and less than 10 In this case the number 3780000 is expressed in scientific notation
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Express 870000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
870000
870000 x 10
870000 x 1012345
87 x 105
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Express 53600 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
25
Express 284000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
26
5 Which is the correct coefficient of 147000 when it is written in scientific notation
A 147B 147C 147D 147
Answer
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
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8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
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10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
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300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
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More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
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13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
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Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
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14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
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15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
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16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
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17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
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19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
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More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
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22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
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23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
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24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
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25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
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26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
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27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
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28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
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32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
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421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
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33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
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34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
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If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
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124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
2
8th Grade Scientific Notation
2015shy11shy20
wwwnjctlorg
3
Table of ContentsClick on the topic to go to that section
bull Purpose of Scientific Notation
bull Magnitude
bull Glossary
bull Writing Numbers in Scientific Notation
bull Converting Between Scientific Notation and Standard Form
bull Comparing Numbers in Scientific Notation
bull Multiply and Divide with Scientific Notation
bull Addition and Subtraction with Scientific Notation
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
4
Purpose ofScientific Notation
Return to Table of Contents
5
Purpose of Scientific Notation
Scientists are often confronted with numbers that look like this300000000000000000000000000000000000000000000000000000 kgCan you guess what weighs this much
6
Blue Whale shy largest animal on earth
The Great Pyramid at Giza
Total Human Population
The Earth
The Sun
2000000000000000000000000000000 kg
60000000000000000000000000 kg
300000000000 kg
600000000 kg
180000 kg
Can you match theseBIG objects to their weights
7
Click object to revealanswer
60000000000000000000000000 kg
2000000000000000000000000000000 kg 300000000000 kg
600000000 kg
180000 kg
Blue Whale shy largest animal on earth
The Great Pyramid at Giza
Total Human Population
The Earth
The Sun
300000000000 kg
Can you match theseBIG objects to their weights
8
grain of sand
steam000000000035 kg
000015 kg
0000000000000000000000000030 kg
molecule
Can you match these small objects to their weights
9
000000000035 kg
000015 kg
Click to reveal the answers
0000000000000000000000000030 kg
grain of sand
steam
molecule
10
The examples were written in standard form the form we normally use But the standard form is difficult to work with when a number is HUGE or tiny if it has a lot of zeros
Scientists have come up with a more convenient method to write very LARGE and very small numbers
Scientific Notation
Writing numbers in scientific notation doesnt change the value of the number
11
Scientific Notation uses Powers of 10 to write big or small numbers more conveniently
Scientific Notation
Using scientific notation requires us to use the rules of exponents we learned earlier While we developed those rules for all bases scientific notation only uses base 10
12
Powers of Ten
Click here to see a video on powers of ten which puts our universe into perspective
Click here to move from the Milky Way through space towards Earth to anoak tree and then within a cell
101 = 10
102 = 10 x 10 = 100
103 = 10 x 10 x 10 = 1000
104 = 10 x 10 x 10 x 10 = 10000
105 = 10 x 10 x 10 x 10 x 10 = 100000
13
Powers of Integers
Powers are a quick way to write repeated multiplication just as multiplication was a quick way to write repeated addition
These are all equivalent
103(10)(10)(10)
1000
In this case the base is 10 and the exponent is 3
14
Review of Exponent RulesRemember that when multiplying numbers with exponents if the bases are the same you write the base and add the exponents
25 x 26 = 2(5+6) = 211
33 x 37 = 3(3+7) = 310
108 x 10shy3 = 10(8+shy3) = 105
47 x 4shy7 = 4(7+shy7) = 40 = 1
15
1 102 x 104 =
A 106
B 108
C 1010
D 1012
Answer
16
2 1014 x 10shy6 =
A 106
B 108
C 1010
D 1012
Answer
17
3 10shy4 x 10shy6 =
A 10shy6
B 10shy8
C 10shy10
D 10shy12
Answer
18
4 104 x 106 =
A 106
B 108
C 1010
D 1012
Answer
19
Writing Numbers in Scientific Notation
Return to Table of Contents
20
Scientific Notation
Here are some different ways of writing 6500
6500 = 65 thousand65 thousand = 65 x 100065 x 1000 = 65 x 103
which means that 6500 = 65 x 103
6500 is standard form of the numberand 65 x 103 is scientific notation
These are two ways of writing the same number
21
Scientific Notation
65 x 103 isnt a lot more convenient than 6500
But lets do the same thing with 7400000000which is equal to 74 billionwhich is 74 x 1000000000which is 74 x 109
Besides being shorter than 7400000000 it is a lot easier to keep track of the zeros in scientific notation
And well see that the math gets a lot easier as well
22
Scientific Notation
Scientific notation expresses numbers as the product of
a coefficient and 10 raised to some power378 x 106
The coefficient is always greater than or equal to one and less than 10 In this case the number 3780000 is expressed in scientific notation
23
Express 870000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
870000
870000 x 10
870000 x 1012345
87 x 105
24
Express 53600 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
25
Express 284000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
26
5 Which is the correct coefficient of 147000 when it is written in scientific notation
A 147B 147C 147D 147
Answer
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
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103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
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124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
3
Table of ContentsClick on the topic to go to that section
bull Purpose of Scientific Notation
bull Magnitude
bull Glossary
bull Writing Numbers in Scientific Notation
bull Converting Between Scientific Notation and Standard Form
bull Comparing Numbers in Scientific Notation
bull Multiply and Divide with Scientific Notation
bull Addition and Subtraction with Scientific Notation
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
4
Purpose ofScientific Notation
Return to Table of Contents
5
Purpose of Scientific Notation
Scientists are often confronted with numbers that look like this300000000000000000000000000000000000000000000000000000 kgCan you guess what weighs this much
6
Blue Whale shy largest animal on earth
The Great Pyramid at Giza
Total Human Population
The Earth
The Sun
2000000000000000000000000000000 kg
60000000000000000000000000 kg
300000000000 kg
600000000 kg
180000 kg
Can you match theseBIG objects to their weights
7
Click object to revealanswer
60000000000000000000000000 kg
2000000000000000000000000000000 kg 300000000000 kg
600000000 kg
180000 kg
Blue Whale shy largest animal on earth
The Great Pyramid at Giza
Total Human Population
The Earth
The Sun
300000000000 kg
Can you match theseBIG objects to their weights
8
grain of sand
steam000000000035 kg
000015 kg
0000000000000000000000000030 kg
molecule
Can you match these small objects to their weights
9
000000000035 kg
000015 kg
Click to reveal the answers
0000000000000000000000000030 kg
grain of sand
steam
molecule
10
The examples were written in standard form the form we normally use But the standard form is difficult to work with when a number is HUGE or tiny if it has a lot of zeros
Scientists have come up with a more convenient method to write very LARGE and very small numbers
Scientific Notation
Writing numbers in scientific notation doesnt change the value of the number
11
Scientific Notation uses Powers of 10 to write big or small numbers more conveniently
Scientific Notation
Using scientific notation requires us to use the rules of exponents we learned earlier While we developed those rules for all bases scientific notation only uses base 10
12
Powers of Ten
Click here to see a video on powers of ten which puts our universe into perspective
Click here to move from the Milky Way through space towards Earth to anoak tree and then within a cell
101 = 10
102 = 10 x 10 = 100
103 = 10 x 10 x 10 = 1000
104 = 10 x 10 x 10 x 10 = 10000
105 = 10 x 10 x 10 x 10 x 10 = 100000
13
Powers of Integers
Powers are a quick way to write repeated multiplication just as multiplication was a quick way to write repeated addition
These are all equivalent
103(10)(10)(10)
1000
In this case the base is 10 and the exponent is 3
14
Review of Exponent RulesRemember that when multiplying numbers with exponents if the bases are the same you write the base and add the exponents
25 x 26 = 2(5+6) = 211
33 x 37 = 3(3+7) = 310
108 x 10shy3 = 10(8+shy3) = 105
47 x 4shy7 = 4(7+shy7) = 40 = 1
15
1 102 x 104 =
A 106
B 108
C 1010
D 1012
Answer
16
2 1014 x 10shy6 =
A 106
B 108
C 1010
D 1012
Answer
17
3 10shy4 x 10shy6 =
A 10shy6
B 10shy8
C 10shy10
D 10shy12
Answer
18
4 104 x 106 =
A 106
B 108
C 1010
D 1012
Answer
19
Writing Numbers in Scientific Notation
Return to Table of Contents
20
Scientific Notation
Here are some different ways of writing 6500
6500 = 65 thousand65 thousand = 65 x 100065 x 1000 = 65 x 103
which means that 6500 = 65 x 103
6500 is standard form of the numberand 65 x 103 is scientific notation
These are two ways of writing the same number
21
Scientific Notation
65 x 103 isnt a lot more convenient than 6500
But lets do the same thing with 7400000000which is equal to 74 billionwhich is 74 x 1000000000which is 74 x 109
Besides being shorter than 7400000000 it is a lot easier to keep track of the zeros in scientific notation
And well see that the math gets a lot easier as well
22
Scientific Notation
Scientific notation expresses numbers as the product of
a coefficient and 10 raised to some power378 x 106
The coefficient is always greater than or equal to one and less than 10 In this case the number 3780000 is expressed in scientific notation
23
Express 870000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
870000
870000 x 10
870000 x 1012345
87 x 105
24
Express 53600 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
25
Express 284000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
26
5 Which is the correct coefficient of 147000 when it is written in scientific notation
A 147B 147C 147D 147
Answer
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
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79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
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89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
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103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
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124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
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Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
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137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
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Attachments
notebook(1801411b2398)galleryitem
4
Purpose ofScientific Notation
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5
Purpose of Scientific Notation
Scientists are often confronted with numbers that look like this300000000000000000000000000000000000000000000000000000 kgCan you guess what weighs this much
6
Blue Whale shy largest animal on earth
The Great Pyramid at Giza
Total Human Population
The Earth
The Sun
2000000000000000000000000000000 kg
60000000000000000000000000 kg
300000000000 kg
600000000 kg
180000 kg
Can you match theseBIG objects to their weights
7
Click object to revealanswer
60000000000000000000000000 kg
2000000000000000000000000000000 kg 300000000000 kg
600000000 kg
180000 kg
Blue Whale shy largest animal on earth
The Great Pyramid at Giza
Total Human Population
The Earth
The Sun
300000000000 kg
Can you match theseBIG objects to their weights
8
grain of sand
steam000000000035 kg
000015 kg
0000000000000000000000000030 kg
molecule
Can you match these small objects to their weights
9
000000000035 kg
000015 kg
Click to reveal the answers
0000000000000000000000000030 kg
grain of sand
steam
molecule
10
The examples were written in standard form the form we normally use But the standard form is difficult to work with when a number is HUGE or tiny if it has a lot of zeros
Scientists have come up with a more convenient method to write very LARGE and very small numbers
Scientific Notation
Writing numbers in scientific notation doesnt change the value of the number
11
Scientific Notation uses Powers of 10 to write big or small numbers more conveniently
Scientific Notation
Using scientific notation requires us to use the rules of exponents we learned earlier While we developed those rules for all bases scientific notation only uses base 10
12
Powers of Ten
Click here to see a video on powers of ten which puts our universe into perspective
Click here to move from the Milky Way through space towards Earth to anoak tree and then within a cell
101 = 10
102 = 10 x 10 = 100
103 = 10 x 10 x 10 = 1000
104 = 10 x 10 x 10 x 10 = 10000
105 = 10 x 10 x 10 x 10 x 10 = 100000
13
Powers of Integers
Powers are a quick way to write repeated multiplication just as multiplication was a quick way to write repeated addition
These are all equivalent
103(10)(10)(10)
1000
In this case the base is 10 and the exponent is 3
14
Review of Exponent RulesRemember that when multiplying numbers with exponents if the bases are the same you write the base and add the exponents
25 x 26 = 2(5+6) = 211
33 x 37 = 3(3+7) = 310
108 x 10shy3 = 10(8+shy3) = 105
47 x 4shy7 = 4(7+shy7) = 40 = 1
15
1 102 x 104 =
A 106
B 108
C 1010
D 1012
Answer
16
2 1014 x 10shy6 =
A 106
B 108
C 1010
D 1012
Answer
17
3 10shy4 x 10shy6 =
A 10shy6
B 10shy8
C 10shy10
D 10shy12
Answer
18
4 104 x 106 =
A 106
B 108
C 1010
D 1012
Answer
19
Writing Numbers in Scientific Notation
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20
Scientific Notation
Here are some different ways of writing 6500
6500 = 65 thousand65 thousand = 65 x 100065 x 1000 = 65 x 103
which means that 6500 = 65 x 103
6500 is standard form of the numberand 65 x 103 is scientific notation
These are two ways of writing the same number
21
Scientific Notation
65 x 103 isnt a lot more convenient than 6500
But lets do the same thing with 7400000000which is equal to 74 billionwhich is 74 x 1000000000which is 74 x 109
Besides being shorter than 7400000000 it is a lot easier to keep track of the zeros in scientific notation
And well see that the math gets a lot easier as well
22
Scientific Notation
Scientific notation expresses numbers as the product of
a coefficient and 10 raised to some power378 x 106
The coefficient is always greater than or equal to one and less than 10 In this case the number 3780000 is expressed in scientific notation
23
Express 870000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
870000
870000 x 10
870000 x 1012345
87 x 105
24
Express 53600 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
25
Express 284000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
26
5 Which is the correct coefficient of 147000 when it is written in scientific notation
A 147B 147C 147D 147
Answer
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
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79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
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89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
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103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
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124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
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Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
5
Purpose of Scientific Notation
Scientists are often confronted with numbers that look like this300000000000000000000000000000000000000000000000000000 kgCan you guess what weighs this much
6
Blue Whale shy largest animal on earth
The Great Pyramid at Giza
Total Human Population
The Earth
The Sun
2000000000000000000000000000000 kg
60000000000000000000000000 kg
300000000000 kg
600000000 kg
180000 kg
Can you match theseBIG objects to their weights
7
Click object to revealanswer
60000000000000000000000000 kg
2000000000000000000000000000000 kg 300000000000 kg
600000000 kg
180000 kg
Blue Whale shy largest animal on earth
The Great Pyramid at Giza
Total Human Population
The Earth
The Sun
300000000000 kg
Can you match theseBIG objects to their weights
8
grain of sand
steam000000000035 kg
000015 kg
0000000000000000000000000030 kg
molecule
Can you match these small objects to their weights
9
000000000035 kg
000015 kg
Click to reveal the answers
0000000000000000000000000030 kg
grain of sand
steam
molecule
10
The examples were written in standard form the form we normally use But the standard form is difficult to work with when a number is HUGE or tiny if it has a lot of zeros
Scientists have come up with a more convenient method to write very LARGE and very small numbers
Scientific Notation
Writing numbers in scientific notation doesnt change the value of the number
11
Scientific Notation uses Powers of 10 to write big or small numbers more conveniently
Scientific Notation
Using scientific notation requires us to use the rules of exponents we learned earlier While we developed those rules for all bases scientific notation only uses base 10
12
Powers of Ten
Click here to see a video on powers of ten which puts our universe into perspective
Click here to move from the Milky Way through space towards Earth to anoak tree and then within a cell
101 = 10
102 = 10 x 10 = 100
103 = 10 x 10 x 10 = 1000
104 = 10 x 10 x 10 x 10 = 10000
105 = 10 x 10 x 10 x 10 x 10 = 100000
13
Powers of Integers
Powers are a quick way to write repeated multiplication just as multiplication was a quick way to write repeated addition
These are all equivalent
103(10)(10)(10)
1000
In this case the base is 10 and the exponent is 3
14
Review of Exponent RulesRemember that when multiplying numbers with exponents if the bases are the same you write the base and add the exponents
25 x 26 = 2(5+6) = 211
33 x 37 = 3(3+7) = 310
108 x 10shy3 = 10(8+shy3) = 105
47 x 4shy7 = 4(7+shy7) = 40 = 1
15
1 102 x 104 =
A 106
B 108
C 1010
D 1012
Answer
16
2 1014 x 10shy6 =
A 106
B 108
C 1010
D 1012
Answer
17
3 10shy4 x 10shy6 =
A 10shy6
B 10shy8
C 10shy10
D 10shy12
Answer
18
4 104 x 106 =
A 106
B 108
C 1010
D 1012
Answer
19
Writing Numbers in Scientific Notation
Return to Table of Contents
20
Scientific Notation
Here are some different ways of writing 6500
6500 = 65 thousand65 thousand = 65 x 100065 x 1000 = 65 x 103
which means that 6500 = 65 x 103
6500 is standard form of the numberand 65 x 103 is scientific notation
These are two ways of writing the same number
21
Scientific Notation
65 x 103 isnt a lot more convenient than 6500
But lets do the same thing with 7400000000which is equal to 74 billionwhich is 74 x 1000000000which is 74 x 109
Besides being shorter than 7400000000 it is a lot easier to keep track of the zeros in scientific notation
And well see that the math gets a lot easier as well
22
Scientific Notation
Scientific notation expresses numbers as the product of
a coefficient and 10 raised to some power378 x 106
The coefficient is always greater than or equal to one and less than 10 In this case the number 3780000 is expressed in scientific notation
23
Express 870000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
870000
870000 x 10
870000 x 1012345
87 x 105
24
Express 53600 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
25
Express 284000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
26
5 Which is the correct coefficient of 147000 when it is written in scientific notation
A 147B 147C 147D 147
Answer
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
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124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
6
Blue Whale shy largest animal on earth
The Great Pyramid at Giza
Total Human Population
The Earth
The Sun
2000000000000000000000000000000 kg
60000000000000000000000000 kg
300000000000 kg
600000000 kg
180000 kg
Can you match theseBIG objects to their weights
7
Click object to revealanswer
60000000000000000000000000 kg
2000000000000000000000000000000 kg 300000000000 kg
600000000 kg
180000 kg
Blue Whale shy largest animal on earth
The Great Pyramid at Giza
Total Human Population
The Earth
The Sun
300000000000 kg
Can you match theseBIG objects to their weights
8
grain of sand
steam000000000035 kg
000015 kg
0000000000000000000000000030 kg
molecule
Can you match these small objects to their weights
9
000000000035 kg
000015 kg
Click to reveal the answers
0000000000000000000000000030 kg
grain of sand
steam
molecule
10
The examples were written in standard form the form we normally use But the standard form is difficult to work with when a number is HUGE or tiny if it has a lot of zeros
Scientists have come up with a more convenient method to write very LARGE and very small numbers
Scientific Notation
Writing numbers in scientific notation doesnt change the value of the number
11
Scientific Notation uses Powers of 10 to write big or small numbers more conveniently
Scientific Notation
Using scientific notation requires us to use the rules of exponents we learned earlier While we developed those rules for all bases scientific notation only uses base 10
12
Powers of Ten
Click here to see a video on powers of ten which puts our universe into perspective
Click here to move from the Milky Way through space towards Earth to anoak tree and then within a cell
101 = 10
102 = 10 x 10 = 100
103 = 10 x 10 x 10 = 1000
104 = 10 x 10 x 10 x 10 = 10000
105 = 10 x 10 x 10 x 10 x 10 = 100000
13
Powers of Integers
Powers are a quick way to write repeated multiplication just as multiplication was a quick way to write repeated addition
These are all equivalent
103(10)(10)(10)
1000
In this case the base is 10 and the exponent is 3
14
Review of Exponent RulesRemember that when multiplying numbers with exponents if the bases are the same you write the base and add the exponents
25 x 26 = 2(5+6) = 211
33 x 37 = 3(3+7) = 310
108 x 10shy3 = 10(8+shy3) = 105
47 x 4shy7 = 4(7+shy7) = 40 = 1
15
1 102 x 104 =
A 106
B 108
C 1010
D 1012
Answer
16
2 1014 x 10shy6 =
A 106
B 108
C 1010
D 1012
Answer
17
3 10shy4 x 10shy6 =
A 10shy6
B 10shy8
C 10shy10
D 10shy12
Answer
18
4 104 x 106 =
A 106
B 108
C 1010
D 1012
Answer
19
Writing Numbers in Scientific Notation
Return to Table of Contents
20
Scientific Notation
Here are some different ways of writing 6500
6500 = 65 thousand65 thousand = 65 x 100065 x 1000 = 65 x 103
which means that 6500 = 65 x 103
6500 is standard form of the numberand 65 x 103 is scientific notation
These are two ways of writing the same number
21
Scientific Notation
65 x 103 isnt a lot more convenient than 6500
But lets do the same thing with 7400000000which is equal to 74 billionwhich is 74 x 1000000000which is 74 x 109
Besides being shorter than 7400000000 it is a lot easier to keep track of the zeros in scientific notation
And well see that the math gets a lot easier as well
22
Scientific Notation
Scientific notation expresses numbers as the product of
a coefficient and 10 raised to some power378 x 106
The coefficient is always greater than or equal to one and less than 10 In this case the number 3780000 is expressed in scientific notation
23
Express 870000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
870000
870000 x 10
870000 x 1012345
87 x 105
24
Express 53600 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
25
Express 284000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
26
5 Which is the correct coefficient of 147000 when it is written in scientific notation
A 147B 147C 147D 147
Answer
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
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124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
7
Click object to revealanswer
60000000000000000000000000 kg
2000000000000000000000000000000 kg 300000000000 kg
600000000 kg
180000 kg
Blue Whale shy largest animal on earth
The Great Pyramid at Giza
Total Human Population
The Earth
The Sun
300000000000 kg
Can you match theseBIG objects to their weights
8
grain of sand
steam000000000035 kg
000015 kg
0000000000000000000000000030 kg
molecule
Can you match these small objects to their weights
9
000000000035 kg
000015 kg
Click to reveal the answers
0000000000000000000000000030 kg
grain of sand
steam
molecule
10
The examples were written in standard form the form we normally use But the standard form is difficult to work with when a number is HUGE or tiny if it has a lot of zeros
Scientists have come up with a more convenient method to write very LARGE and very small numbers
Scientific Notation
Writing numbers in scientific notation doesnt change the value of the number
11
Scientific Notation uses Powers of 10 to write big or small numbers more conveniently
Scientific Notation
Using scientific notation requires us to use the rules of exponents we learned earlier While we developed those rules for all bases scientific notation only uses base 10
12
Powers of Ten
Click here to see a video on powers of ten which puts our universe into perspective
Click here to move from the Milky Way through space towards Earth to anoak tree and then within a cell
101 = 10
102 = 10 x 10 = 100
103 = 10 x 10 x 10 = 1000
104 = 10 x 10 x 10 x 10 = 10000
105 = 10 x 10 x 10 x 10 x 10 = 100000
13
Powers of Integers
Powers are a quick way to write repeated multiplication just as multiplication was a quick way to write repeated addition
These are all equivalent
103(10)(10)(10)
1000
In this case the base is 10 and the exponent is 3
14
Review of Exponent RulesRemember that when multiplying numbers with exponents if the bases are the same you write the base and add the exponents
25 x 26 = 2(5+6) = 211
33 x 37 = 3(3+7) = 310
108 x 10shy3 = 10(8+shy3) = 105
47 x 4shy7 = 4(7+shy7) = 40 = 1
15
1 102 x 104 =
A 106
B 108
C 1010
D 1012
Answer
16
2 1014 x 10shy6 =
A 106
B 108
C 1010
D 1012
Answer
17
3 10shy4 x 10shy6 =
A 10shy6
B 10shy8
C 10shy10
D 10shy12
Answer
18
4 104 x 106 =
A 106
B 108
C 1010
D 1012
Answer
19
Writing Numbers in Scientific Notation
Return to Table of Contents
20
Scientific Notation
Here are some different ways of writing 6500
6500 = 65 thousand65 thousand = 65 x 100065 x 1000 = 65 x 103
which means that 6500 = 65 x 103
6500 is standard form of the numberand 65 x 103 is scientific notation
These are two ways of writing the same number
21
Scientific Notation
65 x 103 isnt a lot more convenient than 6500
But lets do the same thing with 7400000000which is equal to 74 billionwhich is 74 x 1000000000which is 74 x 109
Besides being shorter than 7400000000 it is a lot easier to keep track of the zeros in scientific notation
And well see that the math gets a lot easier as well
22
Scientific Notation
Scientific notation expresses numbers as the product of
a coefficient and 10 raised to some power378 x 106
The coefficient is always greater than or equal to one and less than 10 In this case the number 3780000 is expressed in scientific notation
23
Express 870000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
870000
870000 x 10
870000 x 1012345
87 x 105
24
Express 53600 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
25
Express 284000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
26
5 Which is the correct coefficient of 147000 when it is written in scientific notation
A 147B 147C 147D 147
Answer
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
8
grain of sand
steam000000000035 kg
000015 kg
0000000000000000000000000030 kg
molecule
Can you match these small objects to their weights
9
000000000035 kg
000015 kg
Click to reveal the answers
0000000000000000000000000030 kg
grain of sand
steam
molecule
10
The examples were written in standard form the form we normally use But the standard form is difficult to work with when a number is HUGE or tiny if it has a lot of zeros
Scientists have come up with a more convenient method to write very LARGE and very small numbers
Scientific Notation
Writing numbers in scientific notation doesnt change the value of the number
11
Scientific Notation uses Powers of 10 to write big or small numbers more conveniently
Scientific Notation
Using scientific notation requires us to use the rules of exponents we learned earlier While we developed those rules for all bases scientific notation only uses base 10
12
Powers of Ten
Click here to see a video on powers of ten which puts our universe into perspective
Click here to move from the Milky Way through space towards Earth to anoak tree and then within a cell
101 = 10
102 = 10 x 10 = 100
103 = 10 x 10 x 10 = 1000
104 = 10 x 10 x 10 x 10 = 10000
105 = 10 x 10 x 10 x 10 x 10 = 100000
13
Powers of Integers
Powers are a quick way to write repeated multiplication just as multiplication was a quick way to write repeated addition
These are all equivalent
103(10)(10)(10)
1000
In this case the base is 10 and the exponent is 3
14
Review of Exponent RulesRemember that when multiplying numbers with exponents if the bases are the same you write the base and add the exponents
25 x 26 = 2(5+6) = 211
33 x 37 = 3(3+7) = 310
108 x 10shy3 = 10(8+shy3) = 105
47 x 4shy7 = 4(7+shy7) = 40 = 1
15
1 102 x 104 =
A 106
B 108
C 1010
D 1012
Answer
16
2 1014 x 10shy6 =
A 106
B 108
C 1010
D 1012
Answer
17
3 10shy4 x 10shy6 =
A 10shy6
B 10shy8
C 10shy10
D 10shy12
Answer
18
4 104 x 106 =
A 106
B 108
C 1010
D 1012
Answer
19
Writing Numbers in Scientific Notation
Return to Table of Contents
20
Scientific Notation
Here are some different ways of writing 6500
6500 = 65 thousand65 thousand = 65 x 100065 x 1000 = 65 x 103
which means that 6500 = 65 x 103
6500 is standard form of the numberand 65 x 103 is scientific notation
These are two ways of writing the same number
21
Scientific Notation
65 x 103 isnt a lot more convenient than 6500
But lets do the same thing with 7400000000which is equal to 74 billionwhich is 74 x 1000000000which is 74 x 109
Besides being shorter than 7400000000 it is a lot easier to keep track of the zeros in scientific notation
And well see that the math gets a lot easier as well
22
Scientific Notation
Scientific notation expresses numbers as the product of
a coefficient and 10 raised to some power378 x 106
The coefficient is always greater than or equal to one and less than 10 In this case the number 3780000 is expressed in scientific notation
23
Express 870000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
870000
870000 x 10
870000 x 1012345
87 x 105
24
Express 53600 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
25
Express 284000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
26
5 Which is the correct coefficient of 147000 when it is written in scientific notation
A 147B 147C 147D 147
Answer
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
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124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
9
000000000035 kg
000015 kg
Click to reveal the answers
0000000000000000000000000030 kg
grain of sand
steam
molecule
10
The examples were written in standard form the form we normally use But the standard form is difficult to work with when a number is HUGE or tiny if it has a lot of zeros
Scientists have come up with a more convenient method to write very LARGE and very small numbers
Scientific Notation
Writing numbers in scientific notation doesnt change the value of the number
11
Scientific Notation uses Powers of 10 to write big or small numbers more conveniently
Scientific Notation
Using scientific notation requires us to use the rules of exponents we learned earlier While we developed those rules for all bases scientific notation only uses base 10
12
Powers of Ten
Click here to see a video on powers of ten which puts our universe into perspective
Click here to move from the Milky Way through space towards Earth to anoak tree and then within a cell
101 = 10
102 = 10 x 10 = 100
103 = 10 x 10 x 10 = 1000
104 = 10 x 10 x 10 x 10 = 10000
105 = 10 x 10 x 10 x 10 x 10 = 100000
13
Powers of Integers
Powers are a quick way to write repeated multiplication just as multiplication was a quick way to write repeated addition
These are all equivalent
103(10)(10)(10)
1000
In this case the base is 10 and the exponent is 3
14
Review of Exponent RulesRemember that when multiplying numbers with exponents if the bases are the same you write the base and add the exponents
25 x 26 = 2(5+6) = 211
33 x 37 = 3(3+7) = 310
108 x 10shy3 = 10(8+shy3) = 105
47 x 4shy7 = 4(7+shy7) = 40 = 1
15
1 102 x 104 =
A 106
B 108
C 1010
D 1012
Answer
16
2 1014 x 10shy6 =
A 106
B 108
C 1010
D 1012
Answer
17
3 10shy4 x 10shy6 =
A 10shy6
B 10shy8
C 10shy10
D 10shy12
Answer
18
4 104 x 106 =
A 106
B 108
C 1010
D 1012
Answer
19
Writing Numbers in Scientific Notation
Return to Table of Contents
20
Scientific Notation
Here are some different ways of writing 6500
6500 = 65 thousand65 thousand = 65 x 100065 x 1000 = 65 x 103
which means that 6500 = 65 x 103
6500 is standard form of the numberand 65 x 103 is scientific notation
These are two ways of writing the same number
21
Scientific Notation
65 x 103 isnt a lot more convenient than 6500
But lets do the same thing with 7400000000which is equal to 74 billionwhich is 74 x 1000000000which is 74 x 109
Besides being shorter than 7400000000 it is a lot easier to keep track of the zeros in scientific notation
And well see that the math gets a lot easier as well
22
Scientific Notation
Scientific notation expresses numbers as the product of
a coefficient and 10 raised to some power378 x 106
The coefficient is always greater than or equal to one and less than 10 In this case the number 3780000 is expressed in scientific notation
23
Express 870000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
870000
870000 x 10
870000 x 1012345
87 x 105
24
Express 53600 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
25
Express 284000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
26
5 Which is the correct coefficient of 147000 when it is written in scientific notation
A 147B 147C 147D 147
Answer
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
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124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
10
The examples were written in standard form the form we normally use But the standard form is difficult to work with when a number is HUGE or tiny if it has a lot of zeros
Scientists have come up with a more convenient method to write very LARGE and very small numbers
Scientific Notation
Writing numbers in scientific notation doesnt change the value of the number
11
Scientific Notation uses Powers of 10 to write big or small numbers more conveniently
Scientific Notation
Using scientific notation requires us to use the rules of exponents we learned earlier While we developed those rules for all bases scientific notation only uses base 10
12
Powers of Ten
Click here to see a video on powers of ten which puts our universe into perspective
Click here to move from the Milky Way through space towards Earth to anoak tree and then within a cell
101 = 10
102 = 10 x 10 = 100
103 = 10 x 10 x 10 = 1000
104 = 10 x 10 x 10 x 10 = 10000
105 = 10 x 10 x 10 x 10 x 10 = 100000
13
Powers of Integers
Powers are a quick way to write repeated multiplication just as multiplication was a quick way to write repeated addition
These are all equivalent
103(10)(10)(10)
1000
In this case the base is 10 and the exponent is 3
14
Review of Exponent RulesRemember that when multiplying numbers with exponents if the bases are the same you write the base and add the exponents
25 x 26 = 2(5+6) = 211
33 x 37 = 3(3+7) = 310
108 x 10shy3 = 10(8+shy3) = 105
47 x 4shy7 = 4(7+shy7) = 40 = 1
15
1 102 x 104 =
A 106
B 108
C 1010
D 1012
Answer
16
2 1014 x 10shy6 =
A 106
B 108
C 1010
D 1012
Answer
17
3 10shy4 x 10shy6 =
A 10shy6
B 10shy8
C 10shy10
D 10shy12
Answer
18
4 104 x 106 =
A 106
B 108
C 1010
D 1012
Answer
19
Writing Numbers in Scientific Notation
Return to Table of Contents
20
Scientific Notation
Here are some different ways of writing 6500
6500 = 65 thousand65 thousand = 65 x 100065 x 1000 = 65 x 103
which means that 6500 = 65 x 103
6500 is standard form of the numberand 65 x 103 is scientific notation
These are two ways of writing the same number
21
Scientific Notation
65 x 103 isnt a lot more convenient than 6500
But lets do the same thing with 7400000000which is equal to 74 billionwhich is 74 x 1000000000which is 74 x 109
Besides being shorter than 7400000000 it is a lot easier to keep track of the zeros in scientific notation
And well see that the math gets a lot easier as well
22
Scientific Notation
Scientific notation expresses numbers as the product of
a coefficient and 10 raised to some power378 x 106
The coefficient is always greater than or equal to one and less than 10 In this case the number 3780000 is expressed in scientific notation
23
Express 870000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
870000
870000 x 10
870000 x 1012345
87 x 105
24
Express 53600 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
25
Express 284000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
26
5 Which is the correct coefficient of 147000 when it is written in scientific notation
A 147B 147C 147D 147
Answer
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
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124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
11
Scientific Notation uses Powers of 10 to write big or small numbers more conveniently
Scientific Notation
Using scientific notation requires us to use the rules of exponents we learned earlier While we developed those rules for all bases scientific notation only uses base 10
12
Powers of Ten
Click here to see a video on powers of ten which puts our universe into perspective
Click here to move from the Milky Way through space towards Earth to anoak tree and then within a cell
101 = 10
102 = 10 x 10 = 100
103 = 10 x 10 x 10 = 1000
104 = 10 x 10 x 10 x 10 = 10000
105 = 10 x 10 x 10 x 10 x 10 = 100000
13
Powers of Integers
Powers are a quick way to write repeated multiplication just as multiplication was a quick way to write repeated addition
These are all equivalent
103(10)(10)(10)
1000
In this case the base is 10 and the exponent is 3
14
Review of Exponent RulesRemember that when multiplying numbers with exponents if the bases are the same you write the base and add the exponents
25 x 26 = 2(5+6) = 211
33 x 37 = 3(3+7) = 310
108 x 10shy3 = 10(8+shy3) = 105
47 x 4shy7 = 4(7+shy7) = 40 = 1
15
1 102 x 104 =
A 106
B 108
C 1010
D 1012
Answer
16
2 1014 x 10shy6 =
A 106
B 108
C 1010
D 1012
Answer
17
3 10shy4 x 10shy6 =
A 10shy6
B 10shy8
C 10shy10
D 10shy12
Answer
18
4 104 x 106 =
A 106
B 108
C 1010
D 1012
Answer
19
Writing Numbers in Scientific Notation
Return to Table of Contents
20
Scientific Notation
Here are some different ways of writing 6500
6500 = 65 thousand65 thousand = 65 x 100065 x 1000 = 65 x 103
which means that 6500 = 65 x 103
6500 is standard form of the numberand 65 x 103 is scientific notation
These are two ways of writing the same number
21
Scientific Notation
65 x 103 isnt a lot more convenient than 6500
But lets do the same thing with 7400000000which is equal to 74 billionwhich is 74 x 1000000000which is 74 x 109
Besides being shorter than 7400000000 it is a lot easier to keep track of the zeros in scientific notation
And well see that the math gets a lot easier as well
22
Scientific Notation
Scientific notation expresses numbers as the product of
a coefficient and 10 raised to some power378 x 106
The coefficient is always greater than or equal to one and less than 10 In this case the number 3780000 is expressed in scientific notation
23
Express 870000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
870000
870000 x 10
870000 x 1012345
87 x 105
24
Express 53600 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
25
Express 284000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
26
5 Which is the correct coefficient of 147000 when it is written in scientific notation
A 147B 147C 147D 147
Answer
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
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124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
12
Powers of Ten
Click here to see a video on powers of ten which puts our universe into perspective
Click here to move from the Milky Way through space towards Earth to anoak tree and then within a cell
101 = 10
102 = 10 x 10 = 100
103 = 10 x 10 x 10 = 1000
104 = 10 x 10 x 10 x 10 = 10000
105 = 10 x 10 x 10 x 10 x 10 = 100000
13
Powers of Integers
Powers are a quick way to write repeated multiplication just as multiplication was a quick way to write repeated addition
These are all equivalent
103(10)(10)(10)
1000
In this case the base is 10 and the exponent is 3
14
Review of Exponent RulesRemember that when multiplying numbers with exponents if the bases are the same you write the base and add the exponents
25 x 26 = 2(5+6) = 211
33 x 37 = 3(3+7) = 310
108 x 10shy3 = 10(8+shy3) = 105
47 x 4shy7 = 4(7+shy7) = 40 = 1
15
1 102 x 104 =
A 106
B 108
C 1010
D 1012
Answer
16
2 1014 x 10shy6 =
A 106
B 108
C 1010
D 1012
Answer
17
3 10shy4 x 10shy6 =
A 10shy6
B 10shy8
C 10shy10
D 10shy12
Answer
18
4 104 x 106 =
A 106
B 108
C 1010
D 1012
Answer
19
Writing Numbers in Scientific Notation
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20
Scientific Notation
Here are some different ways of writing 6500
6500 = 65 thousand65 thousand = 65 x 100065 x 1000 = 65 x 103
which means that 6500 = 65 x 103
6500 is standard form of the numberand 65 x 103 is scientific notation
These are two ways of writing the same number
21
Scientific Notation
65 x 103 isnt a lot more convenient than 6500
But lets do the same thing with 7400000000which is equal to 74 billionwhich is 74 x 1000000000which is 74 x 109
Besides being shorter than 7400000000 it is a lot easier to keep track of the zeros in scientific notation
And well see that the math gets a lot easier as well
22
Scientific Notation
Scientific notation expresses numbers as the product of
a coefficient and 10 raised to some power378 x 106
The coefficient is always greater than or equal to one and less than 10 In this case the number 3780000 is expressed in scientific notation
23
Express 870000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
870000
870000 x 10
870000 x 1012345
87 x 105
24
Express 53600 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
25
Express 284000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
26
5 Which is the correct coefficient of 147000 when it is written in scientific notation
A 147B 147C 147D 147
Answer
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
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124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
13
Powers of Integers
Powers are a quick way to write repeated multiplication just as multiplication was a quick way to write repeated addition
These are all equivalent
103(10)(10)(10)
1000
In this case the base is 10 and the exponent is 3
14
Review of Exponent RulesRemember that when multiplying numbers with exponents if the bases are the same you write the base and add the exponents
25 x 26 = 2(5+6) = 211
33 x 37 = 3(3+7) = 310
108 x 10shy3 = 10(8+shy3) = 105
47 x 4shy7 = 4(7+shy7) = 40 = 1
15
1 102 x 104 =
A 106
B 108
C 1010
D 1012
Answer
16
2 1014 x 10shy6 =
A 106
B 108
C 1010
D 1012
Answer
17
3 10shy4 x 10shy6 =
A 10shy6
B 10shy8
C 10shy10
D 10shy12
Answer
18
4 104 x 106 =
A 106
B 108
C 1010
D 1012
Answer
19
Writing Numbers in Scientific Notation
Return to Table of Contents
20
Scientific Notation
Here are some different ways of writing 6500
6500 = 65 thousand65 thousand = 65 x 100065 x 1000 = 65 x 103
which means that 6500 = 65 x 103
6500 is standard form of the numberand 65 x 103 is scientific notation
These are two ways of writing the same number
21
Scientific Notation
65 x 103 isnt a lot more convenient than 6500
But lets do the same thing with 7400000000which is equal to 74 billionwhich is 74 x 1000000000which is 74 x 109
Besides being shorter than 7400000000 it is a lot easier to keep track of the zeros in scientific notation
And well see that the math gets a lot easier as well
22
Scientific Notation
Scientific notation expresses numbers as the product of
a coefficient and 10 raised to some power378 x 106
The coefficient is always greater than or equal to one and less than 10 In this case the number 3780000 is expressed in scientific notation
23
Express 870000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
870000
870000 x 10
870000 x 1012345
87 x 105
24
Express 53600 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
25
Express 284000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
26
5 Which is the correct coefficient of 147000 when it is written in scientific notation
A 147B 147C 147D 147
Answer
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
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124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
14
Review of Exponent RulesRemember that when multiplying numbers with exponents if the bases are the same you write the base and add the exponents
25 x 26 = 2(5+6) = 211
33 x 37 = 3(3+7) = 310
108 x 10shy3 = 10(8+shy3) = 105
47 x 4shy7 = 4(7+shy7) = 40 = 1
15
1 102 x 104 =
A 106
B 108
C 1010
D 1012
Answer
16
2 1014 x 10shy6 =
A 106
B 108
C 1010
D 1012
Answer
17
3 10shy4 x 10shy6 =
A 10shy6
B 10shy8
C 10shy10
D 10shy12
Answer
18
4 104 x 106 =
A 106
B 108
C 1010
D 1012
Answer
19
Writing Numbers in Scientific Notation
Return to Table of Contents
20
Scientific Notation
Here are some different ways of writing 6500
6500 = 65 thousand65 thousand = 65 x 100065 x 1000 = 65 x 103
which means that 6500 = 65 x 103
6500 is standard form of the numberand 65 x 103 is scientific notation
These are two ways of writing the same number
21
Scientific Notation
65 x 103 isnt a lot more convenient than 6500
But lets do the same thing with 7400000000which is equal to 74 billionwhich is 74 x 1000000000which is 74 x 109
Besides being shorter than 7400000000 it is a lot easier to keep track of the zeros in scientific notation
And well see that the math gets a lot easier as well
22
Scientific Notation
Scientific notation expresses numbers as the product of
a coefficient and 10 raised to some power378 x 106
The coefficient is always greater than or equal to one and less than 10 In this case the number 3780000 is expressed in scientific notation
23
Express 870000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
870000
870000 x 10
870000 x 1012345
87 x 105
24
Express 53600 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
25
Express 284000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
26
5 Which is the correct coefficient of 147000 when it is written in scientific notation
A 147B 147C 147D 147
Answer
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
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103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
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124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
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Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
15
1 102 x 104 =
A 106
B 108
C 1010
D 1012
Answer
16
2 1014 x 10shy6 =
A 106
B 108
C 1010
D 1012
Answer
17
3 10shy4 x 10shy6 =
A 10shy6
B 10shy8
C 10shy10
D 10shy12
Answer
18
4 104 x 106 =
A 106
B 108
C 1010
D 1012
Answer
19
Writing Numbers in Scientific Notation
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20
Scientific Notation
Here are some different ways of writing 6500
6500 = 65 thousand65 thousand = 65 x 100065 x 1000 = 65 x 103
which means that 6500 = 65 x 103
6500 is standard form of the numberand 65 x 103 is scientific notation
These are two ways of writing the same number
21
Scientific Notation
65 x 103 isnt a lot more convenient than 6500
But lets do the same thing with 7400000000which is equal to 74 billionwhich is 74 x 1000000000which is 74 x 109
Besides being shorter than 7400000000 it is a lot easier to keep track of the zeros in scientific notation
And well see that the math gets a lot easier as well
22
Scientific Notation
Scientific notation expresses numbers as the product of
a coefficient and 10 raised to some power378 x 106
The coefficient is always greater than or equal to one and less than 10 In this case the number 3780000 is expressed in scientific notation
23
Express 870000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
870000
870000 x 10
870000 x 1012345
87 x 105
24
Express 53600 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
25
Express 284000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
26
5 Which is the correct coefficient of 147000 when it is written in scientific notation
A 147B 147C 147D 147
Answer
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
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103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
16
2 1014 x 10shy6 =
A 106
B 108
C 1010
D 1012
Answer
17
3 10shy4 x 10shy6 =
A 10shy6
B 10shy8
C 10shy10
D 10shy12
Answer
18
4 104 x 106 =
A 106
B 108
C 1010
D 1012
Answer
19
Writing Numbers in Scientific Notation
Return to Table of Contents
20
Scientific Notation
Here are some different ways of writing 6500
6500 = 65 thousand65 thousand = 65 x 100065 x 1000 = 65 x 103
which means that 6500 = 65 x 103
6500 is standard form of the numberand 65 x 103 is scientific notation
These are two ways of writing the same number
21
Scientific Notation
65 x 103 isnt a lot more convenient than 6500
But lets do the same thing with 7400000000which is equal to 74 billionwhich is 74 x 1000000000which is 74 x 109
Besides being shorter than 7400000000 it is a lot easier to keep track of the zeros in scientific notation
And well see that the math gets a lot easier as well
22
Scientific Notation
Scientific notation expresses numbers as the product of
a coefficient and 10 raised to some power378 x 106
The coefficient is always greater than or equal to one and less than 10 In this case the number 3780000 is expressed in scientific notation
23
Express 870000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
870000
870000 x 10
870000 x 1012345
87 x 105
24
Express 53600 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
25
Express 284000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
26
5 Which is the correct coefficient of 147000 when it is written in scientific notation
A 147B 147C 147D 147
Answer
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
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103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
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124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
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Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
17
3 10shy4 x 10shy6 =
A 10shy6
B 10shy8
C 10shy10
D 10shy12
Answer
18
4 104 x 106 =
A 106
B 108
C 1010
D 1012
Answer
19
Writing Numbers in Scientific Notation
Return to Table of Contents
20
Scientific Notation
Here are some different ways of writing 6500
6500 = 65 thousand65 thousand = 65 x 100065 x 1000 = 65 x 103
which means that 6500 = 65 x 103
6500 is standard form of the numberand 65 x 103 is scientific notation
These are two ways of writing the same number
21
Scientific Notation
65 x 103 isnt a lot more convenient than 6500
But lets do the same thing with 7400000000which is equal to 74 billionwhich is 74 x 1000000000which is 74 x 109
Besides being shorter than 7400000000 it is a lot easier to keep track of the zeros in scientific notation
And well see that the math gets a lot easier as well
22
Scientific Notation
Scientific notation expresses numbers as the product of
a coefficient and 10 raised to some power378 x 106
The coefficient is always greater than or equal to one and less than 10 In this case the number 3780000 is expressed in scientific notation
23
Express 870000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
870000
870000 x 10
870000 x 1012345
87 x 105
24
Express 53600 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
25
Express 284000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
26
5 Which is the correct coefficient of 147000 when it is written in scientific notation
A 147B 147C 147D 147
Answer
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
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103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
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Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
18
4 104 x 106 =
A 106
B 108
C 1010
D 1012
Answer
19
Writing Numbers in Scientific Notation
Return to Table of Contents
20
Scientific Notation
Here are some different ways of writing 6500
6500 = 65 thousand65 thousand = 65 x 100065 x 1000 = 65 x 103
which means that 6500 = 65 x 103
6500 is standard form of the numberand 65 x 103 is scientific notation
These are two ways of writing the same number
21
Scientific Notation
65 x 103 isnt a lot more convenient than 6500
But lets do the same thing with 7400000000which is equal to 74 billionwhich is 74 x 1000000000which is 74 x 109
Besides being shorter than 7400000000 it is a lot easier to keep track of the zeros in scientific notation
And well see that the math gets a lot easier as well
22
Scientific Notation
Scientific notation expresses numbers as the product of
a coefficient and 10 raised to some power378 x 106
The coefficient is always greater than or equal to one and less than 10 In this case the number 3780000 is expressed in scientific notation
23
Express 870000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
870000
870000 x 10
870000 x 1012345
87 x 105
24
Express 53600 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
25
Express 284000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
26
5 Which is the correct coefficient of 147000 when it is written in scientific notation
A 147B 147C 147D 147
Answer
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
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Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
19
Writing Numbers in Scientific Notation
Return to Table of Contents
20
Scientific Notation
Here are some different ways of writing 6500
6500 = 65 thousand65 thousand = 65 x 100065 x 1000 = 65 x 103
which means that 6500 = 65 x 103
6500 is standard form of the numberand 65 x 103 is scientific notation
These are two ways of writing the same number
21
Scientific Notation
65 x 103 isnt a lot more convenient than 6500
But lets do the same thing with 7400000000which is equal to 74 billionwhich is 74 x 1000000000which is 74 x 109
Besides being shorter than 7400000000 it is a lot easier to keep track of the zeros in scientific notation
And well see that the math gets a lot easier as well
22
Scientific Notation
Scientific notation expresses numbers as the product of
a coefficient and 10 raised to some power378 x 106
The coefficient is always greater than or equal to one and less than 10 In this case the number 3780000 is expressed in scientific notation
23
Express 870000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
870000
870000 x 10
870000 x 1012345
87 x 105
24
Express 53600 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
25
Express 284000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
26
5 Which is the correct coefficient of 147000 when it is written in scientific notation
A 147B 147C 147D 147
Answer
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
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103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
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124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
20
Scientific Notation
Here are some different ways of writing 6500
6500 = 65 thousand65 thousand = 65 x 100065 x 1000 = 65 x 103
which means that 6500 = 65 x 103
6500 is standard form of the numberand 65 x 103 is scientific notation
These are two ways of writing the same number
21
Scientific Notation
65 x 103 isnt a lot more convenient than 6500
But lets do the same thing with 7400000000which is equal to 74 billionwhich is 74 x 1000000000which is 74 x 109
Besides being shorter than 7400000000 it is a lot easier to keep track of the zeros in scientific notation
And well see that the math gets a lot easier as well
22
Scientific Notation
Scientific notation expresses numbers as the product of
a coefficient and 10 raised to some power378 x 106
The coefficient is always greater than or equal to one and less than 10 In this case the number 3780000 is expressed in scientific notation
23
Express 870000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
870000
870000 x 10
870000 x 1012345
87 x 105
24
Express 53600 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
25
Express 284000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
26
5 Which is the correct coefficient of 147000 when it is written in scientific notation
A 147B 147C 147D 147
Answer
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
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124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
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21
Scientific Notation
65 x 103 isnt a lot more convenient than 6500
But lets do the same thing with 7400000000which is equal to 74 billionwhich is 74 x 1000000000which is 74 x 109
Besides being shorter than 7400000000 it is a lot easier to keep track of the zeros in scientific notation
And well see that the math gets a lot easier as well
22
Scientific Notation
Scientific notation expresses numbers as the product of
a coefficient and 10 raised to some power378 x 106
The coefficient is always greater than or equal to one and less than 10 In this case the number 3780000 is expressed in scientific notation
23
Express 870000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
870000
870000 x 10
870000 x 1012345
87 x 105
24
Express 53600 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
25
Express 284000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
26
5 Which is the correct coefficient of 147000 when it is written in scientific notation
A 147B 147C 147D 147
Answer
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
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79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
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89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
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103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
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124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
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Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
22
Scientific Notation
Scientific notation expresses numbers as the product of
a coefficient and 10 raised to some power378 x 106
The coefficient is always greater than or equal to one and less than 10 In this case the number 3780000 is expressed in scientific notation
23
Express 870000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
870000
870000 x 10
870000 x 1012345
87 x 105
24
Express 53600 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
25
Express 284000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
26
5 Which is the correct coefficient of 147000 when it is written in scientific notation
A 147B 147C 147D 147
Answer
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
23
Express 870000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
870000
870000 x 10
870000 x 1012345
87 x 105
24
Express 53600 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
25
Express 284000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
26
5 Which is the correct coefficient of 147000 when it is written in scientific notation
A 147B 147C 147D 147
Answer
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
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103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
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124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
24
Express 53600 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
25
Express 284000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
26
5 Which is the correct coefficient of 147000 when it is written in scientific notation
A 147B 147C 147D 147
Answer
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
25
Express 284000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
26
5 Which is the correct coefficient of 147000 when it is written in scientific notation
A 147B 147C 147D 147
Answer
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
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124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
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Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
26
5 Which is the correct coefficient of 147000 when it is written in scientific notation
A 147B 147C 147D 147
Answer
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
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89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
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124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
27
6 Which is the correct coefficient of 23400000 when it is written in scientific notation
A 234B 234C 234D 234
Answer
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
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79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
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103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
28
7 How many places do you need to move the decimal point to change 190000 to 19
A 3B 4C 5D 6
Answer
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
29
8 How many places do you need to move the decimal point to change 765200000000 to 7652
A 11B 10C 9D 8
Answer
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
30
9 Which of the following is 345000000 in scientific notation
A 345 x 108
B 345 x 106
C 345 x 106
D 345 x 109
Answer
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
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103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
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124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
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Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
31
10 Which of these numbers written in scientific notation is not a number greater than one
A 34 x 108
B 72 x 103
C 89 x 104
D 22 x 10shy1
E 114 x 1012
F 41 x 103
Answer
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
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89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
32
300000000000000000000000000000000000000000000
000000000 kg
(How do you even say that number)
The Mass of the Solar System
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
33
More Practice
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
34
Express 9040000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
35
Express 13030000 in Scientific Notation
1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
36
Express 1000000000 in Scientific Notation1 Write the number without the comma
2 Place the decimal so that the first number will be less than 10 but greater than or equal to 1
3 Count how many places you had to move the decimal point This becomes the exponent of 10
4 Drop the zeros to the right of the rightshymost nonshyzero digit
Answer
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
37
11 Which of the following is 12300000 in scientific notation
A 123 x 108
B 123 x 105
C 123 x 105
D 123 x 107
Answer
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
38
12 The average distance from Earth to the Moon is approximately 384400000 meters What is the average distance in kilometers from Earth to the Moon written in scientific notation
A 3844 x 104 kilometersB 3844 x 105 kilometersC 3844 x 107 kilometersD 3844 x 108 kilometers
From PARCC PBA sample test calculator 1
Answer
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
39
13 The closest that Venus ever gets to Earth is 38000000 km What is this distance in meters from Venus to Earth written in scientific notation
A 38 x 109 kilometersB 38 x 107 kilometersC 38 x 1010 kilometersD 38 x 106 kilometers A
nswer
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
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Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
40
Writing Small Numbers in
Scientific Notation
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
41
Express 00043 in Scientific Notation
0043
0043 x 10
0043 x 10
123
43 x 10shy3
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this number becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
42
Express 000000832 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
43
Express 00073 in scientific notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
44
Scientific Notation The Difference Between Positive amp Negative Exponents
As you get further and further down a number line in the positive direction your numbers are getting bigger Therefore really big numbers will have a positive exponent when written in scientific notation
As you get further and further down a number line in the negative direction your numbers are getting smaller Therefore really small numbers will have a negative exponent when written in scientific notation
0 20 40 60 80 100 120 140 160 180 200
shy200 shy180 shy160 shy140 shy120 shy100 shy80 shy60 shy40 shy20 0
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
45
14 Which is the correct decimal placement to convert 0000832 to scientific notation
A 832B 832C 832D 832 A
nswer
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
46
15 Which is the correct decimal placement to convert 0000000376 to scientific notation
A 376B 0376C 376D 376 A
nswer
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
47
16 How many times do you need to move the decimal point to change 000658 to 658
A 2B 3C 4D 5 A
nswer
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
48
17 How many times do you need to move the decimal point to change 0000003242 to 3242
A 5B 6C 7D 8
Answer
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
49
18 Write 000278 in scientific notation
A 278 x 10shy4
B 278 x 103
C 278 x 10shy3
D 278 x 10shy3
Answer
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
50
19 Which of these numbers written in scientific notation is a number greater than one
A 34 x 10shy8
B 72 x 10shy3
C 89 x 104
D 22 x 10shy1
E 114 x 10shy12
F 41 x 10shy3
Answer
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
51
More Practice
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
52
Express 0001003 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
53
Express 0000902 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
54
Express 00000012 in Scientific Notation
1 Write the number without the decimal point
2 Place the decimal so that the first number is 1 or more but less than 10
3 Count how many places you had to move the decimal point The negative of this numbers becomes the exponent of 10
4 Drop the zeros to the left of the leftshymost nonshyzero digit
Answer
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
55
20 Write 0000847 in scientific notation
A 847 x 104
B 847 x 10shy4
C 847 x 10shy4
D 847 x 10shy5
Answer
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
56
Converting Between Scientific Notationand Standard Form
Return to Table of Contents
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
57
Express 35 x 104 in Standard Form
35000
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
350000
35
350000
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
58
Express 102 x 106 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
59
Express 342 x 10shy3 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
60
Express 295 x 10shy4 in Standard Form
1 Write the coefficient
2 Add a number of zeros equal to the exponent to the right for positive exponents and to the left for negative
3 Move the decimal the number of places indicated by the exponent to the right for positive exponents and to the left for negative
4 Drop unnecessary zeros and add comma as necessary
Answer
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
61
21 How many times do you need to move the decimal and which direction to change 741 x 10shy6 into standard form A 6 to the rightB 6 to the leftC 7 to the rightD 7 to the left A
nswer
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
62
22 How many times do you need to move the decimal and which direction to change 45 x 10 10 into standard form
A 10 to the rightB 10 to the leftC 11 to the rightD 11 to the left
Answer
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
63
23 Write 646 x 104 in standard form
A 646000B 000000646C 64600D 00000646
Answer
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
64
24 Write 34 x 103 in standard form
A 3400B 340C 34000D 00034 A
nswer
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
65
25 Write 646 x 10 shy5 in standard formA 646000B 000000646C 000646D 00000646 A
nswer
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
66
26 Write 125 x 10shy4 in standard form A 125B 0000125C 000000125D 4125
Answer
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
67
27 Write 456 x 10shy2 in standard form
A 456B 4560C 000456D 00456
Answer
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
68
28 Write 101 x 109 in standard form
A 101000000000B 1010000000C 000000000101D 0000000101
Answer
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
69
This button eliminates the x 10 of a number in scientific notation
So 9 x 108 is entered into the calculator using 9 EE 8 and shows up at the top as 9E8
Using a Calculator for Scientific NotationWhen entering numbers into a calculator that are in scientific notation you can use the EE button It means x 10 to the power of
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
70
Using a Calculator for Scientific NotationEnter the following numbers into the calculator usingthe EE button to determine its value in standard form
a) 4 x 102
b) 57 x 10shy3
c) 987 x 104
d) 143 x 10shy1
Answer
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
71
32E9When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
72
421E-11When reading a calculator that has a number in scientific notation remember that the E stands for x 10 to the power of
Which number written in standard form represents the number in the calculator below
Using a Calculator for Scientific Notation
Answer
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
73
482E10
29 Which number written in standard form represents the number in the calculator below
A 0000000000482
B 00000000000482
C 4820000000000
D 48200000000
Answer
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
74
653E-6
30 Which number written in standard form represents the number in the calculator below
A 0000000653
B 000000653
C 6530000
D 653000000
Answer
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
75
974E-10
31 Which number written in standard form represents the number in the calculator below
A 0000000000974
B 00000000000974
C 9740000000000
D 97400000000
Answer
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
76
407E6
32 Which number written in standard form represents the number in the calculator below
A 000000407
B 0000000407
C 4070000
D 407000000
Answer
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
77
33 Liz saw this number on her calculator screen Which numbers represent the number Liz saw
A 00000006
B 000000006
C shy6000000
D shy60000000
From PARCC EOY sample test calculator 13
Answer
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
78
Magnitude
Return to Table of Contents
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
79
Magnitude
Scientific notation always uses decimal notation that is bigger than 1 but smaller than 10 Why
This is due to magnitude Magnitude is how we can observe very large or very small numbers and easily compare them
The magnitude of a number is the exponent when the number is written in scientific notation Below are a few examples
8304 = 8304 x 103 shy the order of magnitude is 3
20000 = 2 x 104 ndash the order of magnitude is 4
0000034 = 34 x 10shy5 ndash the order of magnitude is shy5
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
80
Write each of the following in Scientific Notation first and then indicate the order of magnitude
6214
47217
813000000
000253
00647
00000049
Scientific Notation Order of Magnitude
Scientific Notation vs Magnitude
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
81
Application
Let J represent the world population in 1950
J = 2556000053
Find the smallest power of 10 that will exceed J
The number above (J) has 10 digits and is smaller than a whole number with 11 digits
(10000000000 or 1010 therefore Jlt1010)
The answer is 10
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
82
Application
Let K represent the national debt in 1950
K = 257357352351
Find the smallest power of 10 that will exceed K
Answer
The number above (K) has 12 digits and is smaller than a whole number with 13 digits
(1000000000000 or 1012 therefore Jlt1012)
The answer is 12
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
83
34 If m = 149162536496481100 find the smallest power of 10 that will exceed m
Derived from( (
Answer
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
84
35 What is the smallest power of 10 that will exceed 5321
Derived from( (
Answer
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
85
36 If m = 628 find the smallest power of 10 that will exceed m
Derived from( (
437562
Answer
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
86
37 What would the negative exponent be used to express the number
Derived from( (1
10000
Answer
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
87
38 The chance of a shark bite is and the chance
of dying from a snake bite is which are more
likely to be bit by
A both a the same
B the snake
C the shark
D neither
Derived from( (1
115000001
50000000
Answer
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
88
Comparing Numbers Written in
Scientific Notation
Return to Table of Contents
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
89
Click for web site
The Scale of the Universe 2
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
90
Comparing Numbers in Scientific Notation
First compare the exponents If the exponents are different the coefficients do not matter they have a smaller effect
Whichever number has the largerexponent is the larger number
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
91
lt gt=
999 x 103 217 x 104
102 x 102 854 x 10shy3
683 x 10shy9 393 x 10shy2
just drag the sign that is correct
Comparing Numbers in Scientific NotationWhen the exponents are different just compare the exponents
Answer
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
92
If the exponents are the same compare the coefficients
The larger the coefficient the larger the number (if the exponents are the same)
Comparing Numbers in Scientific Notation
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
93
567 x 103 467 x 103
When the exponents are the same just compare the coefficients
432 x 106 467 x 106
232 x 1010 323 x 1010
Comparing Numbers in Scientific Notation
lt gt=
Answer
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
94
39 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III I II IV
I 10 x 105
II 75 x 106
III 83 x 104
IV 54 x 107 Answer
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
95
40 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D I II IV III
I 10 x 102
II 75 x 106
III 83 x 109
IV 54 x 107
Answer
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
96
41 Which is ordered from least to greatest
A I II III IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 102
II 75 x 103
III 83 x 10shy2
IV 54 x 10shy3
Answer
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
97
42 Which is ordered from least to greatest
A II III I IV
B IV III I II
C III IV II I
D III IV I II
I 1 x 10shy2
II 75 x 10shy24
III 83 x 10shy15
IV 54 x 102 Answer
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
98
43 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 102
II 75 x 102
III 83 x 102
IV 54 x 102
Answer
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
99
44 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 106
II 75 x 106
IV 54 x 107
III 83 x 106
Answer
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
100
45 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 10 x 103
II 50 x 103
III 83 x 106
IV 95 x 106 Answer
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
101
46 Which is ordered from least to greatest
A I II III IV
B IV III I II
C I IV II III
D III IV I II
I 25 x 10shy3
II 50 x 10shy3
III 92 x 10shy6
IV 42 x 10shy6
Answer
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
102
Multiplying Numbers in Scientific Notation
Return to Table of Contents
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
103
Multiplying with scientific notation requiresat least three (and sometimes four) steps
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Multiplying Numbers in Scientific Notation
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
104
60 x 25 = 15
104 x 102 = 106
15 x 106
15 x 107
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate (60 x 104)(25 x 102)
Multiplying Numbers in Scientific Notation
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
105
Evaluate (480 x 106)(90 x 10shy8)
Multiplying Numbers in Scientific Notation
1 Multiply the coefficients
2 Multiply the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Answer
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
106
47 Evaluate (20 x 10shy4)(40 x 107)Express the result in scientific notation
A 80 x 1011
B 80 x 103
C 50 x 103
D 50 x 1011 E 768 x 10shy28 F 768 x 10shy28
Answer
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
107
48 Evaluate (50 x 106)(70 x 107)
A 35 x 1013 B 35 x 1014 C 35 x 101 D 35 x 10shy1 E 71 x 1013 F 71 x 101
Answer
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
108
49 Evaluate (60 x 102)(20 x 103)
A 12 x 106 B 12 x 101 C 12 x 105
D 30 x 10shy1 E 30 x 105 F 30 x 101
Answer
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
109
50 Evaluate (12 x 10shy6)(25 x 103)Express the result in scientific notation
A 3 x 103
B 3 x 10shy3
C 30 x 10shy3
D 03 x 10shy18
E 30 x 1018
Answer
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
110
51 Evaluate (11 x 104)(34 x 106)Express the result in scientific notation
A 374 x 1024
B 374 x 1010
C 45 x 1024
D 45 x 1010
E 374 x 1024
Answer
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
111
52 Evaluate (33 x 104)(96 x 103)Express the result in scientific notation
A 3168 x 107
B 3168 x 108
C 32 x 107
D 32 x 108
E 30 x 107 Answer
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
112
53 Evaluate (22 x 10shy5)(46 x 10shy4)Express the result in scientific notation
A 1012 x 10shy20
B 1012 x 10shy9
C 1012 x 10shy10
D 1012 x 10shy9
E 1012 x 10shy8
Answer
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
113
Dividing Numbers in Scientific Notation
Dividing with scientific notation follows the same basic rules as multiplying
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
114
Division with Scientific Notation
54 divide 90 = 061 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
106 divide 102 = 104
06 x 104
60 x 103
Evaluate 54 x 10690 x 102
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
115
1 Divide the coefficients
2 Divide the powers of ten applying the rule of exponents
3 Combine those results
4 Put in proper form
Evaluate 44 x 10611 x 10shy3
Division with Scientific Notation
Answer
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
116
54 Evaluate 416 x 10shy9 52 x 10shy5 Express the result in scientific notation
A 08 x 10shy4
B 08 x 10shy14
C 08 x 10shy5
D 8 x 10shy4
E 8 x 10shy5
Answer
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
117
55 Evaluate 76 x 10shy2 4 x 10shy4 Express the result in scientific notation
A 19 x 10shy2
B 19 x 10shy6
C 19 x 102
D 19 x 10shy8
E 19 x 108
Answer
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
118
56 Evaluate 82 x 103 2 x 107 Express the result in scientific notation
A 41 x 10shy10
B 41 x 104
C 41 x 10shy4
D 41 x 1021
E 41 x 1010
Answer
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
119
57 Evaluate 32 x 10shy2 64 x 10shy4 Express the result in scientific notation
A 5 x 10shy6
B 5 x 10shy2
C 5 x 102
D 5 x 101
E 5 x 103
Answer
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
120
58 The point on a pin has a diameter of approximately 1 x 10shy4 meters If an atom has a diameter of 2 x 10shy10 meters about how many atoms could fit across the diameter of the point of a pin
A 50000
B 500000
C 2000000
D 5000000
Question from ADP Algebra I EndshyofshyCourse Practice Test
Answer
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
121
59 The body of a 154 pound person contains approximately 2 X 10shy1 milligrams of gold and 6 X 101 milligrams of aluminum Based on this information the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body
From PARCC EOY sample test nonshycalculator 5
Answer
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
122
60 One type of ant weighs about 3 x 10shy3 gram The ant can carry close to 15 x 10shy1 gram of food on its back The amount of food in grams an ant can carry on its back is approximately how many times its own body weight in grams Give your answer in standard form
From PARCC PBA sample test nonshycalculator 8
Answer
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
123
Addition and Subtraction with Scientific Notation
Return to Table of Contents
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
124
Addition and Subtraction with Scientific Notation
Numbers in scientific notation can only be added or subtracted if they have the same exponents
If needed an intermediary step is to rewrite one of the numbers so it has the same exponent as the other
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
125
Addition and Subtraction
This is the simplest example of addition
40 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
40 x 103 + 53 x 103 = 93 x 103
40 thousand+ 53 thousand93 thousand
This just says
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
126
Addition and Subtraction
This problem is slightly more difficult because you need to add one extra step at the end
80 x 103 + 53 x 103 =
Since the exponents are the same (3) just add the coefficients
80 x 103 + 53 x 103 = 133 x 103
But that is not proper form since 133 gt 10 it should be written as 133 x 104
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
127
Addition and Subtraction
80 x 104 + 53 x 103 =
This requires an extra step at the beginning because the exponents are different We have to either convert the first number to 80 x 103 or the second one to 053 x 104
The latter approach saves us a step at the end
80 x 104 + 053 x 104 = 853 x 104
Once both numbers had the same exponents we just add the coefficient Note that when we made the exponent 1 bigger thats makes the number 10x bigger we had to make the coefficient 110 as large to keep the number the same
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
128
61 The sum of 56 x 103 and 24 x 103 is
A 80 x 103
B 80 x 106
C 80 x 10shy3
D 853 x 103
Answer
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
129
62 ) 80 x 103 minus 20 x 103 is
A 60 x 10shy3
B 60 x 100
C 60 x 103
D 78 x 103
Answer
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
130
63 ) 70 x 103 plus 20 x 102 is
A 90 x 103
B 90 x 105
C 72 x 103
D 72 x 102
Answer
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
131
64 ) 35 x 105 plus 78 x 105 is
A 113 x 105
B 113 x 104
C 113 x 106
D 113 x 1010
Answer
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
132
Glossary
Return to Table of Contents
Teacher N
otes Vocabulary Words are bolded
in the presentation The text box the word is in is then linked to the page at the end of the presentation with the word defined on it
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
133
73
188 29
2154335 112
ten to thepower of 3
103 =
10 x 10 x 10 =
1000
In scientificnotation
the base
will always = 10
The number that is going to be raised to a power It is multiplied the number of times shown in the power
Base
Back to Instruction
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
134
3y
65 x 103
19z 000000459
459 x 10shy7
scientific notationa coefficient
and 10 raised tosome power378 x 106
CoefficientA number used to multiply a variable
A factor of a term
Back to Instruction
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
135
Power
scientific notationa coefficient
and 10 raised tosome power378 x 106
aka Exponent
or Index
ten to thepower of 3
103 = 10 x 10 x 10 =
1000
A number that shows you how many times to use the number in a multiplication
A quick way to write repeated multiplication
Back to Instruction
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
136
A convenient system scientists developed to rewrite big or small numbers using
powers of 10 that does not change the value
big numbers
180000 kg =
18 x 105
small numbers
000015 kg =
15 x 10shy4
a coefficient
and 10 raised to some power
378 x 106
Scientific Notation
Back to Instruction
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
137
A number whose scientific form has been expanded The most familiar form of a number
4500000
000000032
120000
0006789
Standard Form6500
vs
Scientific Form65 x 103
Notethis is not the correct form but the most recognizable
form
Standard Form
Back to Instruction
Attachments
notebook(1801411b2398)galleryitem
Attachments
notebook(1801411b2398)galleryitem