1. 7.NS.2d Convert fractions to decimals using long division.
Warm Up
Write each fraction in the simplest form. 4 12 1 3 18 46 9 23 21 63 1 3
100 72 25 18
or 1 7
Course 2

2. Learn to write fractions as decimals, and vice versa, and to determine whether a decimal is terminating or repeating.

3. Insert Lesson Title Here
Vocabulary
terminating decimal ~ a decimal whose digits end.
Example: ¾ = 0.75
repeating decimal ~ a decimal which has a pattern in their digits that repeat forever.
Example: 1/3 = 0.3

4. 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.

5. Batting Average (thousandths)
Player
Hits
At Bats
Batting Average (thousandths)
Lance Berkman
Alex Rodriguez
Hits
at Bats
172
544
172
544
172 ÷ 544 ≈ 0.316
172
601
172
601
172 ÷ 601 ≈ 0.286
To convert a fraction to a decimal, divide the numerator by the denominator.

6. Additional Example 1: Writing Fractions as Decimals
Write each fraction as a decimal. Round to the nearest hundredth, if necessary. 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

7. 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

8. 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
… = 0.72

9. 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

10. Write each fraction as a decimal. 3 5 A.
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

11. 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 =
Reading Math
You read the decimal as “eighteen thousandths.”

12. 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 =

13. Additional 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.
Fraction
What the Calculator Shows
Completion Rate
1,546
3,875
1546 ÷
ENTER
3875
0.399
His completion rate is

14. Insert Lesson Title Here
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
2,830
5,186
2830 ÷
ENTER
5186
0.546
His completion rate is

15. 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