2-11 Equivalent Fractions and Decimals

Vocabulary

rational number

terminating decimalrepeating decimal

2-11 Equivalent Fractions and Decimals

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.

2-11 Equivalent Fractions and Decimals

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.

2-11 Equivalent Fractions and Decimals

Write each fraction as a decimal. Round to the nearest hundredth, if necessary.

Additional Example 1: Writing Fractions as Decimals

A. 14

1.00 9.0 5.000

B. 95 C. 5

3

4 5 30.2

– 820

– 200

14 = 0.25

5 1

– 540

.8

– 400

95

= 1.8

1

– 3

20

.6

– 1820

– 18

6

20– 18

2

53 ≈ 1.67

6

2-11 Equivalent Fractions and Decimals

You can use a calculator to check your division:

1

9

533

Helpful Hint

÷ 4 = 0.25

÷ 5 = 1.8

÷ 3 = 1.66…

2-11 Equivalent Fractions and Decimals

Check It Out: Example 1

Write each fraction as a decimal. Round to the nearest hundredth, if necessary.

A. 65 B. 7

4 C. 56

6.051.2

–510 1.2

7.0051

–430

.75

–2820 1.75

5.0030

–4820

.8

–182

3

0.83

2-11 Equivalent Fractions and Decimals

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

0.727272… = 0.72

2-11 Equivalent Fractions and Decimals

Write each fraction as a decimal.

Additional Example 2A: Write Fractions as Terminating and Repeating Decimals

A.

25

9 25

______) 9.000.3

–75 The remainder is 0.150

6

–150 0

9 25

= 0.36

This is a terminating decimal.

2-11 Equivalent Fractions and Decimals

Write each fraction as a decimal.

Additional Example 2B: Write Fractions as Terminating and Repeating Decimals

B.

18

17 18

______)17.00

0.9

–162 The pattern repeats.80

4

– 72 8

17 18

= 0.94

This is a repeating decimal.

2-11 Equivalent Fractions and Decimals

Write each fraction as a decimal.

Check It Out: Example 2A

A. 11 4

25 11.00 – 8 30

2.75

–28 20

2.75–20

0

2-11 Equivalent Fractions and Decimals

Write each fraction as a decimal.

Check It Out: Example 2B

A. 29 33

33 29.0000 –264

0.8787

0.87

260 –231

290 –264 260

–23129

2-11 Equivalent Fractions and Decimals

Write each decimal as a fraction in simplest form.

Additional Example 3: Writing Decimals as Fractions

A. 0.018 B. 1.55

0.018 = 181,000 1.55 =

155100

=18 ÷ 2

1,000 ÷ 2=155 ÷ 5

100 ÷ 5

=3120

or 1 1120=

9500

You read the decimal 0.018 as “eighteen thousandths.”

Reading Math

2-11 Equivalent Fractions and Decimals

Check It Out: Example 3

Write each decimal as a fraction in simplest form.

A. 0.065 B. 3.12

0.065 = 651,000

= 65 ÷ 51,000 ÷ 5

= 13200

3.12 =312100

= 312 ÷ 4 100 ÷ 4

7825

or 3 325

7825

=

2-11 Equivalent Fractions and Decimals

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.

Additional Example 4: Sports Application

Fraction What the Calculator Shows Completion Rate

1,5463,875 1546 ÷ 3875 ENTER 0.398967742 0.399

His completion rate is 0.399.

2-11 Equivalent Fractions and Decimals

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.

1115

11 ÷ 15 = 0.73 ≈ 0.733

2-11 Equivalent Fractions and Decimals

Lesson Quiz

Write each fraction as a decimal.

1.

3. 4.

Write each decimal as a fraction in simplest form.

5. 0.42

7. If your soccer team wins 21 out of 30 games,

what is your team’s winning rate?

2.6253.2

2150

69 8

165 2.

218

6. 8.625

0.70

710

1120 0.550.7

5 8

or 8