1. Equivalent Fractions and Decimals
2-10
Equivalent Fractions and Decimals
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. Equivalent Fractions and Decimals
Course 2
2-10
Equivalent Fractions and Decimals
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

3. Equivalent Fractions and Decimals
Course 2
2-10
Equivalent Fractions and Decimals
Problem of the Day
Martin recorded how much a bean plant grew each week. The first week the plant grew of an inch, of an inch the second week, and of an inch the third week. During which week did the plant grow the least? 4 7 7 8 7 9
week 1

4. 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.

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

6. 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.

7. Batting Average (thousandths)
Course 2
2-10
Equivalent Fractions and Decimals
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.

8. Additional Example 1: Writing Fractions as Decimals
Course 2
2-10
Equivalent Fractions and Decimals
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

9. Equivalent Fractions and Decimals
Course 2
2-10
Equivalent Fractions and Decimals
You can use a calculator to check your division: 1 9 5 33
Helpful Hint ÷ 4 =
0.25
1.8 3
1.66…

10. 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

11. Equivalent Fractions and Decimals
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
… = 0.72

12. 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

13. 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

14. 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

15. 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 =

16. Additional Example 4: Sports Application
Course 2
2-10
Equivalent Fractions and Decimals
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

17. Insert Lesson Title Here
Course 2
2-10
Equivalent Fractions and Decimals
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

18. 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