2-10 Equivalent Fractions and Decimals

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm UpWrite each fraction in the simplest form.

1. 2.

3. 4.

Course 2

2-10 Equivalent Fractions and Decimals

1846

2163

10072

13

13

412

923

2518 or 1 7

18

Problem of the Day

Martin recorded how much a bean plant grew each week. The first week the plant grew of an inch, of an inch the second week, and of an inch the third week. During which week did the plant grow the least? week 1

Course 2

2-10 Equivalent Fractions and Decimals

47

78

79

Learn to write fractions as decimals, and vice versa, and to determine whether a decimal is terminating or repeating.

Course 2

2-10 Equivalent Fractions and Decimals

Vocabulary

terminating decimalrepeating decimal

Insert Lesson Title Here

Course 2

2-10 Equivalent Fractions and Decimals

Course 2

2-10 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 on the next slide are for the 2004 Major League Baseball season.

Course 2

2-10 Equivalent Fractions and Decimals

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.

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

Additional Example 1: Writing Fractions as Decimals

Course 2

2-10 Equivalent Fractions and 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

Course 2

2-10 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…

Check It Out: Example 1

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Course 2

2-10 Equivalent Fractions and Decimals

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

Course 2

2-10 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

Write each fraction as a decimal.

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

Course 2

2-10 Equivalent Fractions and Decimals

A.

4 5

4 5

x 2 2

= 8 10

= 0.8

Multiply to get a power of ten in the denominator.

B.

37 50

37 50

x 2 2

= 74 100

= 0.74

Multiply to get a power of ten in the denominator.

Write each fraction as a decimal.

Check It Out: Example 2

Course 2

2-10 Equivalent Fractions and Decimals

A.

3 5

3 5

x 2 2

= 6 10

= 0.6

Multiply to get a power of ten in the denominator.

B.

18 25

18 25

x 4 4

= 72 100

= 0.72

Multiply to get a power of ten in the denominator.

Write each decimal as a fraction in simplest form.

Additional Example 3: Writing Decimals as Fractions

Course 2

2-10 Equivalent Fractions and Decimals

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

Check It Out: Example 3

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Course 2

2-10 Equivalent Fractions and Decimals

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

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

Course 2

2-10 Equivalent Fractions and Decimals

Fraction What the Calculator Shows Completion Rate

1,5463,875 1546 ÷ 3875 ENTER 0.398967742 0.399

His completion rate is 0.399.

Check It Out: Example 4

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Course 2

2-10 Equivalent Fractions and Decimals

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.

Fraction What the Calculator Shows Completion Rate

2,8305,186 2830 ÷ 5186 ENTER 0.54569996 0.546

His completion rate is 0.546.

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

Insert Lesson Title Here

2150

69 8

Course 2

2-10 Equivalent Fractions and Decimals

165 2.

218

6. 8.625

0.70

710

1120 0.550.7

5 8

or 8