Page 302 - Basic College Mathematics with Early Integers

S E C T ION 4 .1 I INTRODUCTION TO DECIMALS 279

Notice that the number of decimal places in a decimal number is the same as
the number of zeros in the denominator of the equivalent fraction. We can use this
fact to write decimals as fractions.
31 7
0.31 = 0.007 =
3 100 3 1000
3 3
æ c æ c
2 decimal 2 zeros 3 decimal 3 zeros
places places

Example 7 Write 0.43 as a fraction. PRACTICE 7
43 Write 0.037 as a fraction.
Solution: 0.43 =
100
c c
2 2
decimal places zeros
Work Practice 7

Example 8 Write 5.7 as a mixed number. PRACTICE 8
Write 14.97 as a mixed number.
7
Solution: 5.7 = 5
10
c c
1 1
decimal place zero
Work Practice 8

Examples Write each decimal as a fraction or a mixed number. Write your PRACTICE 9–11
answer in simplest form. Write each decimal as a
1 fraction or mixed number.
125 125 1
9. 0.125 = = = Write your answer in simplest
1000 8 # 125 8
1 form.
1 9. 0.12
5 5 1 1
10. 23.5 = 23 = 23 = 23 = 23 10. 57.8
#
10 2 # 5 2 1 2
1 11. -209.086
83
11. -105.083 =-105
1000
Work Practice 9–11

Later in the chapter, we write fractions as decimals. If you study Examples 7–11,
you already know how to write fractions with denominators of 10, 100, 1000, and so
on, as decimals.

Objective Comparing Decimals

One way to compare positive decimals is by comparing digits in corresponding places.
5 8
To see why this works, let’s compare 0.5 or and 0.8 or . We know
10 10
5 8
6 since 5 6 8, so Answers
10 10
37 97 3
T T 7. 8. 14 9.
0.5 6 0.8 since 5 6 8 1000 100 25
4 43
This leads to the following. 10. 57 5 11. -209 500