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2-10 Equivalent Fractions and Decimals
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
2-10 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
2-10 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
2-10 Equivalent Fractions and Decimals
Learn to write fractions as decimals, and vice versa, and to determine whether a decimal is terminating or repeating.
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 2006 Major League Baseball season.
2-10 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.
2-10 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
2-10 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…
2-10 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
2-10 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
2-10 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.
2-10 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.
2-10 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
2-10 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
2-10 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.
2-10 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.
2-10 Equivalent Fractions and Decimals
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
2-10 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
2-10 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
2-10 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
2-10 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
2-10 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