Objective1. To write very large or very small numbers in

standard form, in scientific notation, and vice versa.

• To compare and order numbers in scientific notation

Designed by Skip Tyler, Varina High School

How wide is our universe?210,000,000,000,000,000,000,000 miles

(22 zeros)

This number is written in decimal notation. When numbers get this large,

it is easier to write them in scientific notation.

Scientific Notation

A number is expressed in scientific notation when it is in the form

a x 10n

where a is between 1 and 10

and n is an integer

Write the width of the universe in scientific notation.

210,000,000,000,000,000,000,000 miles

Where is the decimal point now?

After the last zero.

Where would you put the decimal to make this number be between 1 and 10?

Between the 2 and the 1

2.10,000,000,000,000,000,000,000.

How many decimal places did you move the decimal?

23When the original number is more than 1,

the exponent is positive.The answer in scientific notation is

2.1 x 1023

1) Express 0.0000000902 in scientific notation.

Where would the decimal go to make the number be between 1 and 10?

9.02The decimal was moved how many places?

8When the original number is less than 1, the

exponent is negative.9.02 x 10-8

Why does a Negative Exponent give us a small number?

10,000 = 10 x 10 x 10 x 10 = 104

1,000 = 10 x 10 x 10 = 103

100 = 10 x 10 = 102

10 = 101 1 = 100 Do you see a pattern?

Sooooo = 10-1

= = 10-2

= = 10-3

= = 10-4

Write 28750.9 in scientific notation.

1. 2.87509 x 10-5

2. 2.87509 x 10-4

3. 2.87509 x 104

4. 2.87509 x 105

2) Express 1.8 x 10-4 in decimal notation.0.00018

3) Express 4.58 x 106 in decimal notation.

4,580,000

On the graphing calculator, scientific notation is done with the button.

4.58 x 106 is typed 4.58 6

4) Use a calculator to evaluate: 4.5 x 10-5

1.6 x 10-2

Type 4.5 -5 1.6 -2

You must include parentheses if you don’t use those buttons!!

(4.5 x 10 -5) (1.6 x 10 -2)

0.0028125Write in scientific notation.

2.8125 x 10-3

5) Use a calculator to evaluate: 7.2 x 10-9

1.2 x 102

On the calculator, the answer is:6.E -11

The answer in scientific notation is 6 x 10 -11

The answer in decimal notation is 0.00000000006

6) Use a calculator to evaluate (0.0042)(330,000).

On the calculator, the answer is1386.

The answer in decimal notation is

1386

The answer in scientific notation is

1.386 x 103

7) Use a calculator to evaluate (3,600,000,000)(23).

On the calculator, the answer is:

8.28 E +10

The answer in scientific notation is

8.28 x 10 10

The answer in decimal notation is

82,800,000,000

Write (2.8 x 103)(5.1 x 10-7) in scientific notation.

1. 14.28 x 10-4

2. 1.428 x 10-3

3. 14.28 x 1010

4. 1.428 x 1011

Write in PROPER scientific notation.(Notice the number is not between 1 and 10)

8) 234.6 x 109

2.346 x 1011

9) 0.0642 x 104

on calculator: 642

6.42 x 10 2

Write 531.42 x 105 in scientific notation.

1. .53142 x 102

2. 5.3142 x 103

3. 53.142 x 104

4. 531.42 x 105

5. 53.142 x 106

6. 5.3142 x 107

7. .53142 x 108

PERFORMING PERFORMING CALCULATIONS CALCULATIONS IN SCIENTIFIC IN SCIENTIFIC

NOTATIONNOTATION

MULTIPLYING AND DIVIDINGMULTIPLYING AND DIVIDING

Rule for Multiplication

When multiplying with scientific notation:

• Multiply the coefficients together.

• Add the exponents.

• The base will remain 10.

(2 x 103) • (3 x 105) =

6 x 108

(4.6x108) (5.8x106) =26.68x1014

Notice: What is wrong with this example?

Although the answer is correct, the number is not in scientific notation.

To finish the problem, move the decimal one

space left and increase the exponent by

one.

26.68x1014 = 2.668x1015

((9.2 x 105) x (2.3 x 107) =

21.16 x 1012 =

2.116 x 1013

(3.2 x 10-5) x (1.5 x 10-3) =

4.8 • 10-8

Rule for Division

When dividing with scientific notation

1. Divide the coefficients

2. Subtract the exponents.

3. The base will remain 10.

(8 • 106) ÷ (2 • 103) =

4 x 103

Please multiply the following numbers.

(5.76 x 102) x (4.55 x 10-4) =

(3 x 105) x (7 x 104) =

(5.63 x 108) x (2 x 100) =

(4.55 x 10-14) x (3.77 x 1011) =

(8.2 x10-6) x (9.4 x 10-3) =

Please multiply the following numbers.

(5.76 x 102) x (4.55 x 10-4) =

(3 x 105) x (7 x 104) =

(5.63 x 108) x (2 x 100) =

(4.55 x 10-14) x (3.77 x 1011) =

(8.2 x10-6) x (9.4 x 10-3) =

2.62 x 10-1

2.1 x 1010

1.13 x 109

7.71 x 10-8

1.72 x 10-2

1. (5.76 x 102) / (4.55 x 10-4) =

2. (3 x 105) / (7 x 104) =

3. (5.63 x 108) / (2) =

4. (8.2 x 10-6) / (9.4 x 10-3) =

5. (4.55 x 10-14) / (3.77 x 1011) =

Please divide the following numbers.

1. (5.76 x 102) / (4.55 x 10-4) = 1.27 x 106

2. (3 x 105) / (7 x 104) = 4.3 x 100 = 4.3

3. (5.63 x 108) / (2 x 100) = 2.82 x 108

4. (8.2 x 10-6) / (9.4 x 10-3) = 8.7 x 10-4

5. (4.55 x 10-14) / (3.77 x 1011) = 1.2 x 10-

25

Please divide the following numbers.

PERFORMING PERFORMING CALCULATIONS CALCULATIONS IN SCIENTIFIC IN SCIENTIFIC

NOTATIONNOTATION

Raising Numbers in Scientific Raising Numbers in Scientific Notation To A PowerNotation To A Power

(5 X 104)2 =

(5 X 104) X (5 X 104) = (5 X 5) X (104 X 104) = (25) X 108 = 2.5 X 109

1. (3.45 X 1010)2

2. (4 X 10-5)2

3. (9.81 X 1021)2

Try These:

1. (3.45 X 1010)2 = (3.45 X 3.45) X (1010 X 1010) = (11.9) X (1020) = 1.19 X 1021

2. (4 X 10-5)2 = (4 X 4) X (10-5 X 10-5) = (16) X (10-10) = 1.6 X 10-9

3. (9.81 X 1021)2 = (9.81 X 9.81) X (1021 X 1021) = (96.24) X (1042) = 9.624 X 1043

1.19 X 1021

1.6 X 10-9

9.624 X 1043

9.54x107 miles

1.86x107 milesper second

Scientific Notation Makes These Numbers Easy