2-6 Equivalent Fractions and Decimals

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

2-6 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

2-6 Equivalent Fractions and Decimals

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

47

78

79

2-6 Equivalent Fractions and Decimals

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

2-6 Equivalent Fractions and Decimals

Vocabulary

terminating decimalrepeating decimal

2-6 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 2006 Major League Baseball season.

2-6 Equivalent Fractions and Decimals

Player HitsAt

BatsBatting Average (thousandths)

Miguel Cabrera

Ichiro Suzuki

Hitsat Bats

195 ÷ 576 ≈ 0.339

224 ÷ 695 ≈ 0.322

195 576195576

224 695 224695

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

2-6 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

2-6 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…

2-6 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

2-6 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

2-6 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

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.

2-6 Equivalent Fractions and Decimals

Write each fraction as a decimal.

Check It Out: Example 2

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.

2-6 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

2-6 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

2-6 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.

2-6 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.

Fraction What the Calculator Shows Completion Rate

2,8305,186 2830 ÷ 5186 ENTER 0.54569996 0.546

His completion rate is 0.546.

2-6 Equivalent Fractions and Decimals

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

2-6 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

2-6 Equivalent Fractions and Decimals

1. Which of the following represents the

fraction as a decimal?

A. 3.4

B. 3.5

C. 3.6

D. 3.7

Lesson Quiz for Student Response Systems

18 5

2-6 Equivalent Fractions and Decimals

2. Which of the following represents the

fraction as a decimal?

A. 0.65

B. 0.75

C. 0.85

D. 0.95

Lesson Quiz for Student Response Systems

13 20

2-6 Equivalent Fractions and Decimals

3. Which of the following represents the decimal 0.32 as a fraction in simplest form?

A. C.

B. D.

Lesson Quiz for Student Response Systems

8 25

7 25

6 25

1 5

2-6 Equivalent Fractions and Decimals

4. Which of the following represents the decimal 6.125 as a fraction in simplest form?

A. or 8 C. or 6

B. or 6 D. or 6

Lesson Quiz for Student Response Systems

49 6

49 8

37 6

31 5

1 6

1 8

1 6

1 5

2-6 Equivalent Fractions and Decimals

5. If Rita scores 34 out of 50 in a class test, what is Rita’s scoring rate?

A. 0.65

B. 0.66

C. 0.67

D. 0.68

Lesson Quiz for Student Response Systems