1. Equivalent Fractions and Decimals
2-10
Equivalent Fractions and Decimals
Course 2
TERMINATING AND REPEATING DECIMALS

2. Course 2
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.

3. Insert Lesson Title Here
Course 2
2-10
Equivalent Fractions and Decimals
Insert Lesson Title Here
Vocabulary
terminating decimal
repeating decimal

4. Additional Example 1: Writing Fractions as Decimals
Course 2
2-10
Equivalent Fractions and Decimals
Additional Example 1: Writing Fractions as Decimals
To convert a fraction to a decimal, divide the numerator by the denominator. . 1 4 9 5 5 3 A. B. C. 1 .8 1 .6 6 6
0.2 5
1.00 4 5
9.0 3
5.000
– 8
– 3
– 5 20 40 20
– 20
– 40
– 18 20
– 18 1 4 9 5
= 1.8 5 3
= 0.25 20
≈ 1.67
– 18 2

5. Insert Lesson Title Here
Course 2
2-10
Equivalent Fractions and Decimals
Insert Lesson Title Here
Check It Out: Example 1
Write each fraction as a decimal. Round to the nearest hundredth, if necessary. 3 4 6 5 7 3 A. B. C. 1 .2 2 .3 3 3
0.7 5
3.00 4 5
6.0 3
7.000
– 2 8
– 6
– 5 20 10 10
– 20
– 10
– 9 10
– 9 3 4 6 5
= 1.2 7 3
= 0.75 10
≈ 2.33
– 9 1

6. Equivalent Fractions and Decimals
Course 2
2-10
Equivalent Fractions and Decimals
The decimals 0.25 and 1.8 in Example 1 are terminating decimals because the decimals comes to an end. The decimal 2.333…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
… = 0.72

7. Additional Example 2: Using Mental Math to Write Fractions as Decimals
Course 2
2-10
Equivalent Fractions and Decimals
Additional Example 2: Using Mental Math to Write Fractions as Decimals
Write each fraction as a decimal.
4 5 A.
4 5
2 2
8 10
Multiply to get a power of ten in the denominator. x =
= 0.8
37 50 B.
37 50
2 2
74 100
Multiply to get a power of ten in the denominator. x =
= 0.74

8. Equivalent Fractions and Decimals
Course 2
2-10
Equivalent Fractions and Decimals
Check It Out: Example 2
Write each fraction as a decimal.
3 5 A.
3 5
2 2
6 10
Multiply to get a power of ten in the denominator. x =
= 0.6
18 25 B.
18 25
4 4
72 100
Multiply to get a power of ten in the denominator. x =
= 0.72

9. Additional Example 3: Writing Decimals as Fractions
Course 2
2-10
Equivalent Fractions and Decimals
Additional Example 3: Writing Decimals as Fractions
Write each decimal as a fraction in simplest form. A
B. 1.55 18
1,000
155
100
0.018 =
1.55 =
18 ÷ 2
1,000 ÷ 2
155 ÷ 5
100 ÷ 5 = = 9
500 31 20 11 20 =
or 1 =
You read the decimal as “eighteen thousandths.”
Reading Math

10. Insert Lesson Title Here
Course 2
2-10
Equivalent Fractions and Decimals
Insert Lesson Title Here
Check It Out: Example 3
Write each decimal as a fraction in simplest form. A
B. 1.30 15
1,000
130
100
0.015 =
1.30 =
15 ÷ 5
1,000 ÷ 5
130 ÷ 10
100 ÷ 10 = = 3
200 3 10 = 13 10
or 1 =

11. Insert Lesson Title Here
Course 2
2-10
Equivalent Fractions and Decimals
Insert Lesson Title Here
Lesson Quiz
Write each fraction as a decimal. 1.
Write each decimal as a fraction in simplest form.
7. If your soccer team wins 21 out of 30 games, what is your team’s winning rate? 16 5 21 8
3.2 2.
2.625 7 10 11 20
0.7
0.55 21 50 69 8
5 8
or 8
0.70