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2-10. Equivalent Fractions and Decimals. Course 2. Warm Up. Problem of the Day. Lesson Presentation. 2-10. Equivalent Fractions and Decimals. Course 2. Learn to write fractions as decimals, and vice versa, and to determine whether a decimal is terminating or repeating. 2-10. - PowerPoint PPT Presentation
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2-10 Equivalent Fractions and Decimals
Course 2
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
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
Insert Lesson Title Here
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
Insert Lesson Title Here
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
Insert Lesson Title Here
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.
