Multiply and Divide in Scientific Notation

Honors Math – Grade 7

The state of Wyoming is rectangular, with a length of about 5.8 x 105 meters and a width of about 4.5 x 105 meters. About how many square meters is the area of Wyoming? Write your answer in scientific notation.

What is the formula for the area of a rectangle?

To find the area of a rectangle, multiply length and width.

)105.4)(108.5( 55 A

Let’s take a closer look at how to multiply numbers in scientific notation.

)105.4)(108.5( 55 A

To multiply numbers in scientific notation:

First, GROUP decimal factors with decimal factors and powers of 10 with powers of 10. )1010)(5.48.5( 55AMultiply the decimals.

5.4

8.5

Multiply the powers of 10 by adding their exponents.

Be sure the resulting product is expressed in scientific notation!

)101.3)(103.2( 94 A

To multiply numbers in scientific notation:

First, GROUP decimal factors with decimal factors and powers of 10 with powers of 10. )1010)(1.33.2( 94 AMultiply the decimals.

1.3

3.2

Multiply the powers of 10 by adding their exponents.

Be sure the resulting product is expressed in scientific notation!

)108)(107.5( 125 A

To multiply numbers in scientific notation:

First, GROUP decimal factors with decimal factors and powers of 10 with powers of 10. )1010)(87.5( 125 AMultiply the decimals.

8

7.5

Multiply the powers of 10 by adding their exponents.

Be sure the resulting product is expressed in scientific notation!

The population of the state of Wyoming is about 510,000. If the land in Wyoming, 2.61 x 1011 square meters, were divided equally among the people living there, how many square meters of land would each person get?

To find how many square meters, divide.

000,510

1061.2 11

Let’s take a closer look at how to divide numbers in scientific notation.

000,510

1061.2 115

11

101.5

1061.2

To divide numbers in scientific notation…

First, GROUP decimal factors with decimal factors and powers of 10 with powers of 10.

511 10101.561.2 Divide the decimals.

61.21.5

Divide the powers of 10 by subtracting their exponents.

Be sure the resulting product is expressed in scientific notation!

9

8

105.2

105.7

To divide numbers in scientific notation…

First, GROUP decimal factors with decimal factors and powers of 10 with powers of 10.

98 10105.25.7 Divide the decimals.

5.75.2

Divide the powers of 10 by subtracting their exponents.

Be sure the resulting product is expressed in scientific notation!

4

5

106.1

1072.6

To divide numbers in scientific notation…

First, GROUP decimal factors with decimal factors and powers of 10 with powers of 10.

45 10106.172.6 Divide the decimals.

72.66.1

Divide the powers of 10 by subtracting their exponents.

Be sure the resulting product is expressed in scientific notation!