1. Vocabulary
rational number
terminating decimal
repeating decimal

2. In baseball, a player’s batting average compares the number of hits with the number of times the player has been at bat. The statistics below are for the 2006 Major League Baseball season.

3. A rational number is a number that can be written as a fraction with an integer for its numerator and a nonzero integer for its denominator. To write a rational number as a decimal, divide the numerator by the denominator.

4. Additional Example 1: Writing Fractions as Decimals
Write each fraction as a decimal. Round to the nearest hundredth, if necessary. 1 4 9 5 5 3 A. B. C. 1 .8 1 .6 6 6
0.2 5
1.00 4 5
9.0 3
5.000
– 8
– 3
– 5 20 40 20
– 20
– 40
– 18 20
– 18 1 4 9 5
= 1.8 5 3
= 0.25 20
≈ 1.67
– 18 2

5. You can use a calculator to check your division: 1 9 5 Helpful Hint33
Helpful Hint ÷ 4 =
0.25
1.8 3
1.66…

6. Check It Out: Example 1
Write each fraction as a decimal. Round to the nearest hundredth, if necessary. 6 5 7 4 5 6 A. B. C.
6.0 5
1.2 –5 10
7.00 5 1 –4 30
.75
–28 20
1.75
5.00 3
–48 20 .8
–18 2
0.83

7. The decimals 0.75 and 1.2 in Example 1 are terminating decimals because the decimals comes to an end. The decimal 0.333…is a repeating decimal because the decimal repeats a pattern forever. You can also write a repeating decimal with a bar over the repeating part.
0.333… = 0.3
0.8333… = 0.83
… = 0.72

8. Write each fraction as a decimal. 9 25 A. 0. 3 6 25 9.00
Additional Example 2A: Write Fractions as Terminating and Repeating Decimals
Write each fraction as a decimal. 9 25 A. 0. 3 6
______ ) 25
9.00
–75
The remainder is 0.
150
–150
This is a terminating decimal.
9 25
= 0.36

9. Write each fraction as a decimal. 17 18 B. 0. 9 4 18 17.00
Additional Example 2B: Write Fractions as Terminating and Repeating Decimals
Write each fraction as a decimal. 17 18 B. 0. 9 4
______ ) 18
17.00
–162
The pattern repeats. 80
– 72
This is a repeating decimal. 8
= 0.94
17 18

10. Check It Out: Example 2A
Write each fraction as a decimal. 11 4 A. 25
11.00
– 8 30 2. 7 5
–28 20
2.75
–20

11. Check It Out: Example 2B
Write each fraction as a decimal. 29 33 A. 33
–264
0.8787
0.87
260
–231
290 29

12. Additional Example 3: Writing Decimals as Fractions
Write each decimal as a fraction in simplest form. A
B. 1.55 18
1,000
155
100
0.018 =
1.55 =
18 ÷ 2
1,000 ÷ 2
155 ÷ 5
100 ÷ 5 = = 9
500 31 20 11 20
or 1 = =
You read the decimal as “eighteen thousandths.”
Reading Math

13. Check It Out: Example 3
Write each decimal as a fraction in simplest form. A
B. 3.12
0.065 = 65
1,000 =
65 ÷ 5
1,000 ÷ 5 13
200
3.12 =
312
100 =
312 ÷ 4
100 ÷ 4 78 25
or 3 3

14. Additional Example 4: Sports Application
A football player completed 1,546 of the 3,875 passes he attempted. Find his completion rate. Write your answer as a decimal rounded to the nearest thousandth.
Fraction
What the Calculator Shows
Completion Rate
1,546
3,875
1546 ÷
ENTER
3875
0.399
His completion rate is

15. Check It Out: Example 4
A basketball player made 11 out of 15 free-throw shots. Find her success rate. Write your answer as a decimal rounded to the nearest thousandth. 11 15 ÷ =
0.73 ≈
0.733

16. Write each fraction as a decimal. 1. 3. 4.
Lesson Quiz
Write each fraction as a decimal. 1.
Write each decimal as a fraction in simplest form.
7. If your soccer team wins 21 out of 30 games, what is your team’s winning rate? 16 5 21 8
3.2 2.
2.625 7 10 11 20
0.7
0.55 21 50 69 8
5 8
or 8
0.70