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 decimal

repeating decimal

A decimal that comes to an end.

A decimal that repeats a pattern forever.

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.

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

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.

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

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.

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

8 is in the thousandths place

5 is in the hundredths place

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.

Example 4: Sports Application

0.3989…

His completion rate is 0.399.

Divide the numerator by the denominator.

15463875 0.399≈

Holt CA Course 1

3-5 Equivalent Fractions and Decimals

Check It Out! Example 1

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

6.0

65

5

1

– 510

.2

– 100

65

= 1.2

Holt CA Course 1

3-5 Equivalent Fractions and Decimals

Write each fraction as a decimal.

Check It Out! Example 2

18 25

18 25

×4 4

=

= 0.72

Multiply to get a power of ten in the denominator. 72

100

Holt CA Course 1

3-5 Equivalent Fractions and Decimals

Check It Out! Example 3

Write each decimal as a fraction in simplest form.

1.30

1.30 =130100

= 130 ÷ 10100 ÷ 10

= 1310

or 1 310

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.