negative exponents and scientific notation chapter 4.2
TRANSCRIPT
Negative Exponents and Scientific Notation
Chapter 4.2
x-a =
= xax-a1
1xa
Negative Exponents
a.
x12
1
1. Write with positive exponents.
x-12
b.
w5
1
1. Write with positive exponents.
w-5
z-2
z2
1
1. Write with positive exponents.
c.
a.
43
1
641
2. Evaluate.
4-3
b.
24
1
161
2. Evaluate.
2-4
w4
a.
3
w-4
3
3. Simplify. Write the expression with no negative exponents.
b.
x6
z-2
x-6
y4z2
3. Simplify. Write the expression with no negative exponents.
y4
c.
x6y5
1
3. Simplify. Write the expression with no negative exponents.
x-6y-5
a. (
(2)-2
4x8
y10
x-8 y10
4. Write with positive exponents.
2x4y-5) -2
Use the power rules.Evaluate and write with positive exponents.
b.
y2
y2
y-3
y3z4
z6
y5
z2
4. Write with positive exponents.
z-4
z-6
Write with positive exponents.Use the quotient rule.Use the product rule.
x-a =
= xax-a1
1xa
Negative Exponents
Scientific Notation
a
a is a number so that 1 ≤ a < 10
n is an integer
x 10n
Two methods to change a number into Scientific Notation
1. Move the decimal point left or right. The number of places is n (left is positive, right is negative)
a x 10n
2. n represents the place value of the first nonzero digit from the original number.
109 108 107 106 105 104 103 102 101 100 10-1 10-2 10-3 10-4 10-5 10-6
Here are the place names.These are the exponential form for each place.
billions
hundred millions
ten millions
millions
hundred thousands
ten thousands
thousands
hundreds
tens
ones
tenths
hundredths
thousandths
ten thousandths
hundred thousandths
millionths
.
x 104
a. 78,200
78200.
7.82
5. Write in scientific notation.
Count the number of places to move.Positive 4 is the exponent.
x 104a. = 7.82
billions
hundred millions
ten millions
millions
hundred thousands
ten thousands
thousands
hundreds
tens
ones
tenths
hundredths
thousandths
ten thousandths
hundred thousandths
millionths
.
109 108 107 106 105 104 103 102 101 100 10-1 10-2 10-3 10-4 10-5 10-6
5. Write in scientific notation.
8,2007
What is the place value of 7?
b. 4,786,000
4786000.
x 1064.786
5. Write in scientific notation.
Count the number of places to move.Positive 6 is the exponent.
5. Write in scientific notation.
x 106b. = 4.786
billions
hundred millions
ten millions
millions
hundred thousands
ten thousands
thousands
hundreds
tens
ones
tenths
hundredths
thousandths
ten thousandths
hundred thousandths
millionths
.
109 108 107 106 105 104 103 102 101 100 10-1 10-2 10-3 10-4 10-5 10-6
,786,0604
What is the place value of4?
a. 0.98
098.
x 10-19.8
6. Write in scientific notation.
Count the number of places to move.Negative 1 is the exponent.
6. Write in scientific notation.
x 10-1a. = 9.8
billions
hundred millions
ten millions
millions
hundred thousands
ten thousands
thousands
hundreds
tens
ones
tenths
hundredths
thousandths
ten thousandths
hundred thousandths
millionths
.
109 108 107 106 105 104 103 102 101 100 10-1 10-2 10-3 10-4 10-5 10-6
0. 89
What is the place value of 9?
b. 0.000092
0000092.
x 10-59.2
6. Write in scientific notation.
Count the number of places to move.Negative 5 is the exponent.
6. Write in scientific notation.
x 10-5b. = 9.2
billions
hundred millions
ten millions
millions
hundred thousands
ten thousands
thousands
hundreds
tens
ones
tenths
hundredths
thousandths
ten thousandths
hundred thousandths
millionths
.
109 108 107 106 105 104 103 102 101 100 10-1 10-2 10-3 10-4 10-5 10-6
0.0000 29
What is the place value of 9?
a. 1.93 x 10
193.
1,930,000
0000
7. Write in decimal notation.
The exponent is positive 6.Move the decimal point right 6 places.
6
a. 1.93 x = 1,930,000
billions
hundred millions
ten millions
millions
hundred thousands
ten thousands
thousands
hundreds
tens
ones
tenths
hundredths
thousandths
ten thousandths
hundred thousandths
millionths
.
109 108 107 106 105 104 103 102 101 100 10-1 10-2 10-3 10-4 10-5 10-6
7. Write in decimal notation.
106
What is the place value of 1?
b. 8.562 x 10
8562.
0.00008562
00000
7. Write in decimal notation.
The exponent is negative 5.Move the decimal point left 5 places.
-5
7. Write in decimal notation.
b. 8.562 x = 0.00008562
billions
hundred millions
ten millions
millions
hundred thousands
ten thousands
thousands
hundreds
tens
ones
tenths
hundredths
thousandths
ten thousandths
hundred thousandths
millionths
.
109 108 107 106 105 104 103 102 101 100 10-1 10-2 10-3 10-4 10-5 10-6
10-5
What is the place value of 8?
8. Astronomers measure distances to faraway galaxies in parsecs. A parsec is 30,900,000,000,000,000 meters, Write this in scientific notation.
30900000000000000.
3.09 x 1016 m
Using Scientific Notation
a x 10n
a is a number so that 1 ≤ a < 10
n is an integer
)1.4
9. Use scientific notation and the laws of exponents to find the following. Leave your answer in scientific notation.
a. (
(
7.84 x 1013
(
56,000)(1,400,000,000)
5.6 x 104) x 109
Write each in scientific notation.
Use the product rule.Multiply the numbers.
b.
9. Use scientific notation and the laws of exponents to find the following. Leave your answer in scientific notation.
3.7
0.3 x
0.0001110.00000037
1.11 x 10-4
x 10-7
Write each in scientific notation.
Write as positive exponents.Divide the numbers.
=
107
104
b.
9. Use scientific notation and the laws of exponents to find the following. Leave your answer in scientific notation.
3.7
0.3 x
0.0001110.00000037
1.11 x 10-4
x 10-7
Write in scientific notation.
Use the product rule.Use the quotient rule.
=
107
104
3 x 10-1 x 103
3 x 102
1013
10. The average from Earth to the distant star Betelgeuse . would it take a space probe to travel from Earth to Betelgeuse at a ? Round to three significant digits.
=(3.09 x 1013)
t = ds
(159)(50000)
((
distanceis 159 parsecs
(1 parsec = 3.09 x 1013 km)speed of 50,000 kilometers per hour
How many hours
Write in scientific notation.
Multiply and use the product rule.
1.59 x 102) 3.09 x )5 x 104
4.9131x 1015
5 x 104
0.98262=
9.83
x
≈
9.8262 x
x 1010
Divide and use the quotient rule.
Write in scientific notation.
4.9131x 1015
5 x 104
Round to three significant digits.
1011
x 10-1
Use the product rule.
1011
Using Scientific Notation
a x 10n
a is a number so that 1 ≤ a < 10
n is an integer
Scientific Notation
a x 10n
a is a number so that 1 ≤ a < 10
n is an integer
Negative Exponents and Scientific Notation
Chapter 4.2