Post on 27-Dec-2015
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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.