Beginning Algebra, 11th Edition

(b)

(c) Move 3 places to the left.

The exponent tells the number of places and the direction that the decimal

point is moved. NOW TRY

7.04* 10 -^3 = 0. 00704

4.283* 106 =4.283 000 = 4,283,000

314 CHAPTER 5 Exponents and Polynomials

OBJECTIVE 3 Use scientific notation in calculations.

Multiplying and Dividing with Scientific Notation

Perform each calculation.

(a)

Commutative and associative properties Multiply; product rule Write 35 in scientific notation. Associative property Product rule Write without exponents.

(b) NOW TRY

4 * 10 -^5

2 * 103

=

4

2

*

10 -^5

103

= 2 * 10 -^8 =0.00000002

=350,000,000

=3.5* 108

=3.5 1101 1072

= 1 3.5 1012 107

= 35 * 107

= 17 521103 1042

17 103215 1042

EXAMPLE 3

Move 6 places to the right. Attach zeros as necessary.

NOW TRY
EXERCISE 3
Perform each calculation.
Write answers in scientific
notation and also without
exponents.

(a)

(b)

18 * 10 -^3

6 * 104

16 107217 10 -^42

NOTE Multiplying or dividing numbers written in scientific notation may produce

an answer in the form Since For example,

Also, if then For example, we could write 1,000,000 as

instead of 1* 106.

a=1, a* 10 n= 10 n. 106

18 10 -^4215 1042 = 40 * 100 = 40. 100 = 1

a 100. 100 =1,a 100 =a.

Don’t stop! This number is notin scientific notation, since 35 is not between 1 and 10.

NOW TRY
EXERCISE 4
See Example 4.About how
much would 8,000,000
nanometers measure in inches?

Using Scientific Notation to Solve an Application

A nanometer is a very small unit of measure that is equivalent to about

0.00000003937 in. About how much would 700,000 nanometers measure in inches?

(Source: World Almanac and Book of Facts.)

Write each number in scientific notation, and then multiply.

Write in scientific notation. Properties of real numbers Multiply; product rule Write 27.559 in scientific notation. Product rule Write without exponents.

Thus, 700,000 nanometers would measure

2.7559* 10 -^2 in., or 0.027559 in. NOW TRY

=0.027559

=2.7559 * 10 -^2

= 1 2.7559 1012 10 -^3

=27.559 * 10 -^3

= 17 3.937 21105 10 -^82

= 17 10521 3.937 10 -^82

700,000 1 0.00000003937 2

EXAMPLE 4

NOW TRY ANSWERS

(a)57,100 (b)0.0000272

(a)
(b)

3.1496* 10 -^1 in., or 0.31496 in.

3 * 10 -^7 , or 0.0000003

4.2* 104 , or 42,000

NOW TRY
EXERCISE 2
Write each number without
exponents.

(a)

(b)2.72* 10 -^5

5.71* 104

Don’t stop here.

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