1. 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

2. VOCABULARY CARDS Fraction to Decimal Decimal to Fraction
Terminating Decimal
Repeating Decimal

3. Batting Average (thousandths)
In baseball, a player’s batting average compares the number of hits with the number of times the player has been at bat.
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.

4. Teacher 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
1A.
1B.
1C. 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 5 3
= 1.8
= 0.25 20
≈ 1.67
– 18 2

5. Student Practice 1:
Write each fraction as a decimal. Round to the nearest hundredth, if necessary. 3 4 6 5 7 3
1A.
1B.
1C. 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 7 3
= 1.2
= 0.75 10
≈ 2.33
– 9 1

6. 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
… = 0.72

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

8. Write each fraction as a decimal.
Student Practice 2:
Write each fraction as a decimal.
3 5
2A.
3 5
2 2
6 10
Multiply to get a power of ten in the denominator. × =
= 0.6
18 25
2B.
18 25
4 4
72 100
Multiply to get a power of ten in the denominator. × =
= 0.72

9. 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.

10. Teacher Example 3: Writing Decimals as Fractions
Write each decimal as a fraction in simplest form. 3A
3B. 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

11. Student Practice 3:
Write each decimal as a fraction in simplest form. 3A
3B. 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 =

12. Teacher 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.
His completion rate is

13. Student Practice 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

14. Write each fraction as a decimal. 1. 3. 4.
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