1. 4.4 Decimals and Fractions
I can convert between decimals and fractions.

2. Write the day of the month as the product of two factors.
Review of Factors
Write the day of the month as the product of two factors.
Possible answer: 12th of the month, 6  2

3. Vocabulary
mixed number
terminating decimal
repeating decimal

4. 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

5. 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

6. 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.

7. 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. 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 =

9. 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 __

10. 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