4-4 Decimals and Fractions

Learn to convert between decimals and fractions.

4-4 Decimals and Fractions

Vocabulary

mixed numberterminating decimalrepeating decimal

4-4 Decimals and Fractions

A number that contains both a whole number greater than 0 and a fraction, such as 1 , is called a mixed number.

34

__

__41

1 1__21

1 __43

2 __41

2 __21

Mixed numbers12

14

34

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5

4-4 Decimals and Fractions

Additional Example 1A: Writing Decimals as Fractions or Mixed Numbers

Write each decimal as a fraction or mixed number.

0.67

Identify the place value of the digit farthest to the right.

The 7 is in the hundredths place, so use 100 as the denominator.

0.67

100____67 Remember!

One

s

Ten

ths

Hun

dred

ths

Tho

usan

dths

Place Value

4-4 Decimals and Fractions

Additional Example 1B: Writing Decimals as Fractions or Mixed Numbers

Write each decimal as a fraction or mixed number.

5.9

Identify the place value of the digit farthest to the right.Write the whole number, 5. The 9 is in the tenths place, so use 10 as the denominator.

5.9

10 ___ 9

5

4-4 Decimals and Fractions

Check It Out: Example 1A

Write each decimal as a fraction or mixed number.

0.73

Identify the place value of the digit farthest to the right.

The 3 is in the hundredths place, so use 100 as the denominator.

0.73

100____73

4-4 Decimals and Fractions

Check It Out: Example 1B

Write each decimal as a fraction or mixed number.

4.8

Identify the place value of the digit farthest to the right.Write the whole number, 4. The 8 is in the tenths place, so use 10 as the denominator.

4.8

10 ___ 8

4

4-4 Decimals and Fractions

Additional Example 2A: Writing Fractions as Decimals

Write each fraction or mixed number as a decimal.

Divide 3 by 20.

Add zeros after the decimal point.

0 20____ 3

The remainder is 0.

.00- 20

.1320

100- 100

5

0

20____ 3

= 0.15

4-4 Decimals and Fractions

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

Writing Math

4-4 Decimals and Fractions

Additional Example 2B: Writing Fractions as Decimals

Divide 1 by 3.

Add zeros after the decimal point.

0 3 __ 1

The 3 repeats in the quotient.

.000- 9

.31 3

10- 9

3

10

=

6

- 9

3

1 3 __ 1

6 6.333… = 6.3_

Write each fraction or mixed number as a decimal.

4-4 Decimals and Fractions

Check It Out: Example 2A

Write each fraction or mixed number as a decimal.

Divide 5 by 20.

Add zeros after the decimal point.

0

20____ 5

The remainder is 0.

.00- 40

.25 20

100- 100

5

0

20____ 5

= 0.25

4-4 Decimals and Fractions

Check It Out: Example 2B

Write each fraction or mixed number as a decimal.

Divide 2 by 3.

Add zeros after the decimal point.

0

3 __ 2

The 6 repeats in the quotient.

.000- 18

.62 3

20- 18

6

20

=

7

- 18

6

2 3 __ 2

7 7.666… = 7.6_

4-4 Decimals and Fractions

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

0.80.750.60.60.50.40.30.250.2

Common Fractions and Equivalent Decimals1

3__1

5__ 1

4__ 2

5__ 1

2__ 3

5__ 2

3__ 3

4__ 4

5__

4-4 Decimals and Fractions

Additional Example 3: Comparing and Ordering Fractions and Decimals

Order the fractions and decimals from least to greatest.

, 0.8, 7 __10

3__4

First rewrite the fractions as decimals. = 0.75 = 0.7

Order the three decimals.

3 __ 4

0

7 __10

__107

3 __ 4

0.75 0.80.7

The numbers in order from least to greatest are , , and 0.8. 710

3 4

4-4 Decimals and Fractions

Check It Out: Example 3

Order the fractions and decimals from least to greatest.

, 0.35, 1 __ 4

1__2

First rewrite the fractions as decimals. = 0.5 = 0.25

Order the three decimals.

1 __ 2

0

1 __ 4

1__ 2

The numbers in order from least to greatest are , 0.35, and . 1 __ 4

1 __ 2

0.35 0.50.25

1 __ 4