3-5 Equivalent Fractions and Decimals
California
Standards
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
Holt CA Course 1
3-5 Equivalent Fractions and Decimals
Vocabulary
terminating decimal
A decimal that comes to an end.
repeating decimal
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.
Hits
At
Bats
Lance Berkman 172
544
Alex Rodriguez
601
Player
172
Hits
At Bats
172
544
172
601
Batting Average
(thousandths)
172 ÷ 544 ≈ 0.316
172 ÷ 601 ≈ 0.286
To convert a fraction to a decimal, divide the
numerator by the denominator.
Holt CA Course 1
3-5 Equivalent Fractions and Decimals
Example 1: Writing Fractions as Decimals
Write each fraction as a decimal. Round to the
nearest hundredth, if necessary.
1
A. 4
0.2 5
4 1.00
–8
20
– 20
0
1 = 0.25
4
Holt CA Course 1
9
B. 5
1.8
5 9.0
–5
40
– 40
0
9 = 1.8
5
5
C. 3
1 .66 6
3 5.000
–3
20
– 18
20
– 18
5
20 3 ≈ 1.67
– 18
2
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
Example 2: Using Mental Math to Write Fractions as
Decimals
Write each fraction as a decimal.
4
A. 5
Multiply to get a power of
4 ×2 = 8
10
ten in the denominator.
5 2
37
B. 50
= 0.8
37 × 2 = 74
50 2
100
= 0.74
Holt CA Course 1
Multiply to get a power of
ten in the denominator.
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
Example 3: Writing Decimals as Fractions
Write each decimal as a fraction in simplest form.
A. 0.018
8 is in the thousandths
place
18
0.018 =
1,000
18 ÷ 2
=
1,000 ÷ 2
9
=
500
B. 1.55
5 is in the hundredths
place
155
1.55 = 100
= 155 ÷ 5
100 ÷ 5
31 or 1 11
=
20
20
Reading Math
You read the decimal 0.018 as “eighteen thousandths.”
Holt CA Course 1
3-5 Equivalent Fractions and Decimals
Example 4: Sports Application
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.
0.3989…
Divide the numerator by
the denominator.
1546
≈ 0.399
3875
His completion rate is 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
5
1.2
5 6.0
–5
10
– 10
0
6 = 1.2
5
Holt CA Course 1
3-5 Equivalent Fractions and Decimals
Check It Out! Example 2
Write each fraction as a decimal.
18
25
18
4 = 72
×
25
4
100
= 0.72
Holt CA Course 1
Multiply to get a power of
ten in the denominator.
3-5 Equivalent Fractions and Decimals
Check It Out! Example 3
Write each decimal as a fraction in simplest
form.
1.30
130
1.30 =
100
= 130 ÷ 10
100 ÷ 10
3
13
or
1
=
10
10
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.
0.5456…
Divide the numerator by
the denominator.
His completion rate is 0.546.
Holt CA Course 1