1. Learn to convert between decimals and fractions.1

2. Vocabulary
mixed number
terminating decimal
repeating decimal 2

3. A number that contains both a whole number greater than 0 and a fraction, such as 1 , is called a mixed number. __ 3 4
Mixed numbers
1 4
1 2
3 4 __ 4 1 1 __ 2 1 __ 4 3 2 __ 4 1 2 __ 1 3

4. Additional Example 1A: Writing Decimals as Fractions or Mixed Numbers
Write each decimal as a fraction or mixed number.
0.67
0.67
Identify the place value of the digit farthest to the right.
100
____ 67
The 7 is in the hundredths place, so use 100 as the denominator.
Remember!
Ones
Tenths
Hundredths
Thousandths
Place Value 4

5. Additional Example 1B: Writing Decimals as Fractions or Mixed Numbers
Write each decimal as a fraction or mixed number.
5.9
5.9
Identify the place value of the digit farthest to the right. 10
___ 9 5
Write the whole number, 5. The 9 is in the tenths place, so use 10 as the denominator. 5

6. Write each decimal as a fraction or mixed number.
Check It Out: Example 1A
Write each decimal as a fraction or mixed number.
0.73
0.73
Identify the place value of the digit farthest to the right.
100
____ 73
The 3 is in the hundredths place, so use 100 as the denominator. 6

7. Write each decimal as a fraction or mixed number.
Check It Out: Example 1B
Write each decimal as a fraction or mixed number.
4.8
4.8
Identify the place value of the digit farthest to the right. 10
___ 8 4
Write the whole number, 4. The 8 is in the tenths place, so use 10 as the denominator. 7

8. Additional Example 2A: Writing Fractions as Decimals
Write each fraction or mixed number as a decimal. 20
____ 3 .1 5
Divide 3 by 20. 20 3
.00
Add zeros after the decimal point.
- 20
100
- 100
The remainder is 0. 20
____ 3 =
0.15 8

9. Writing Math
To write a repeating decimal, you can show three dots or draw a bar over the repeating part: 0.666… = 0.6 9

10. Additional Example 2B: Writing Fractions as Decimals
Write each fraction or mixed number as a decimal. 3 __ 1 6 .3 3 3
Divide 1 by 3. 3 1
.000
Add zeros after the decimal point.
- 9 10
The 3 repeats in the quotient.
- 9 10
- 9
6.333… = 6.3 _ 1 3 __ 1 6 = 10

11. Write each fraction or mixed number as a decimal.
Check It Out: Example 2A
Write each fraction or mixed number as a decimal. 20
____ 5 .2 5
Divide 5 by 20. 20 5
.00
Add zeros after the decimal point.
- 40
100
- 100
The remainder is 0. 20
____ 5 =
0.25 11

12. Write each fraction or mixed number as a decimal.
Check It Out: Example 2B
Write each fraction or mixed number as a decimal. 3 __ 2 7 .6 6 6
Divide 2 by 3. 3 2
.000
Add zeros after the decimal point.
- 18 20
The 6 repeats in the quotient.
- 18 20
- 18
7.666… = 7.6 _ 2 3 __ 2 7 = 12

13. Common Fractions and Equivalent Decimals
A terminating decimal, such as 0.75, has a finite number of decimal places. A repeating decimal, such as 0.666…, has a block of one or more digits that repeat continuously
0.8
0.75
0.6
0.5
0.4
0.3
0.25
0.2
Common Fractions and Equivalent Decimals 1 5 __ 1 4 __ 1 3 __ 2 5 __ 1 2 __ 3 5 __ 2 3 __ 3 4 __ 4 5 __ 13

14. Additional Example 3: Comparing and Ordering Fractions and Decimals
Order the fractions and decimals from least to greatest. __ 3 __ 7
, 0.8, 4 10 3 __ 4 __ 10 7
First rewrite the fractions as decimals = = 0.7
Order the three decimals. 7 __ 10 3 __ 4
0.7
0.75
0.8
The numbers in order from least to greatest are , , and 0.8. 7 10 3 4 14

15. Order the fractions and decimals from least to greatest.
Check It Out: Example 3
Order the fractions and decimals from least to greatest. 1 1 __ 4
, 0.35, __ 2 1 __ 2 1 __ 4
First rewrite the fractions as decimals = = 0.25
Order the three decimals. 1 __ 4 1 __ 2
0.25
0.35
0.5 1 __ 4 1 __
The numbers in order from least to greatest are , 0.35, and 2 15