6th Grade Math Textbook, Fundamentals

Simplify. Write the product in scientific notation.

Multiply: 4(3.98    10 ^5 )

(4 3.98)    10 ^5 Use the Associative Property.

15.92   10 ^5 Multiply.

(1.592  101 )   10 ^5 Express 15.92 in scientific notation.

1.592 (10^1 10 ^5 ) Use the Associative Property.

1.592   10 [1 (5)] Apply the Law of Exponents for Multiplication.

1.592   10 ^4

So 4(3.98   10 ^5 ) 1.592     10 ^4.

1

Check: 4(3.98   10 ^5 )

4(3.98 0.00001)

4(0.0000398)

0.0001592

1.592   10 ^4

1.592   10 ^4 1.592   10 ^4 Tr u e

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4-11

Operations with Scientific Notation

Objective To multiply and divide numbers in scientific notation by a whole number •To use a

calculator to multiply and divide numbers in scientific notation by a whole number

Earth travels at an average speed of 6.7 104 mi/h in its

orbit around the Sun. What is the average distance

around the Sun that Earth travels in 7 hours?

To find the average distance, multiply: (6.7 104 ) 7

To multiply a number expressed in scientific notation

and a whole number, multiply the whole number and

the decimal factor. Express the product in scientific

notation. Then multiply the powers of 10.

Multiply:(6.7   104 )   7

(6.7 7)     104 Use the Commutative and Associative Properties.

46.9    104 Multiply the whole number and the decimal factor.

(4.69   101 )   104 Express 46.9 in scientific notation.

4.69 (10^1  104 ) Use the Associative Property, then multiply.

4.69    101 ^4 Apply the Law of Exponents for Multiplication.

4.69    105

Check: (6.7     104 )   7

(6.7 10,000)    7 Write the power of 10 in standard form.

67,000  7 Multiply 6.7 10,000.

469,000 Multiply 67,000 7.

4.69    105 Write 469,000 in scientific notation.

4.69    105 4.69   105 Tr u e

So Earth travels 469,000, or 4.69   105 , miles around the Sun in 7 hours.

Remember:

Law of Exponents for

Multiplication

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