Holt CA Course 1

3-5 Equivalent Fractions and Decimals

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Holt CA Course 1

3-5 Equivalent Fractions and Decimals

Warm UpWrite each fraction in the simplest form.

1. 2.

3. 4.

1846

2163

10072

13

13

412

923

2518 or 1 7

18

Holt CA Course 1

3-5 Equivalent Fractions and Decimals

Preparation for NS1.1 Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line.Also covered: NS2.4

California Standards

Holt CA Course 1

3-5 Equivalent Fractions and Decimals

Vocabulary

terminating decimalrepeating decimal

Holt CA Course 1

3-5 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.

Player HitsAt

BatsBatting Average (thousandths)

Lance Berkman

Alex Rodriguez

HitsAt Bats

172 ÷ 544 ≈ 0.316

172 ÷ 601 ≈ 0.286

172 544172544

172 601 172601

To convert a fraction to a decimal, divide the numerator by the denominator.

Holt CA Course 1

3-5 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

Holt CA Course 1

3-5 Equivalent Fractions and Decimals

Check It Out! Example 1

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

A. 34

3.00 6.0 7.000

B. 65 C. 7

3

4 5 30.7

– 2 820

– 200

34 = 0.75

5 1

– 510

.2

– 100

65

= 1.2

2

– 6

10

.3

– 910– 9

3

10– 9

1

73 ≈ 2.33

3

Holt CA Course 1

3-5 Equivalent Fractions and Decimals

The decimals 0.75 and 1.2 are terminating decimals because the decimals comes to an end. The decimal 0.333… is a repeating decimal because it includes a group of one or more digits (where all digits are not zero) that repeats 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

Holt CA Course 1

3-5 Equivalent Fractions and Decimals

Write each fraction as a decimal.

Additional Example 2: Using Mental Math to Write Fractions as Decimals

A.

4 5

4 5

×2 2

=

= 0.8

Multiply to get a power of ten in the denominator.

B.

37 50

37 50

×2 2

=

= 0.74

Multiply to get a power of ten in the denominator.

8 10

74 100

Holt CA Course 1

3-5 Equivalent Fractions and Decimals

Write each fraction as a decimal.

Check It Out! Example 2

A.

3 5

3 5

×2 2

=

= 0.6

Multiply to get a power of ten in the denominator.

B.

18 25

18 25

× 4 4

=

= 0.72

Multiply to get a power of ten in the denominator.

6 10

72 100

Holt CA Course 1

3-5 Equivalent Fractions and Decimals

You can also use place value to write a terminating decimal as a fraction. Use the place value of the last digit to the right of the decimal point as the denominator of the fraction.

Holt CA Course 1

3-5 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

Holt CA Course 1

3-5 Equivalent Fractions and Decimals

Check It Out! Example 3

Write each decimal as a fraction in simplest form.

A. 0.015 B. 1.30

0.015 = 151,000 1.30 =130

100

= 15 ÷ 51,000 ÷ 5

= 130 ÷ 10100 ÷ 10

= 1310

or 1 310

= 3200

Holt CA Course 1

3-5 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

0.3989…

His completion rate is 0.399.

Divide the numerator by the denominator.

Holt CA Course 1

3-5 Equivalent Fractions and Decimals

Check It Out! Example 4

Johnny Unitas, a former professional quarterback, completed 2,830 of the 5,186 passes he attempted. Find his completion rate. Write your answer as a decimal rounded to the nearest thousandth.

His completion rate is 0.546.

0.5456… Divide the numerator by the denominator.

Holt CA Course 1

3-5 Equivalent Fractions and DecimalsLesson 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