# Changing fractions to decimals

Remind your children that decimals are another way to represent a fraction. You can show this by reviewing the tenths, hundredths and thousandths on the base 10 number system. Decimals are simply so many tenths or hundredths or thousandths.

You can review the relationship between decimals and common fractions using these examples that explain how to change from decimals to fractions.

They show how fractions with denominators of 10, 100, 1000 are written as decimals.

## Fractions to decimals - tenths, hundredths, thousandths

Changing fractions that have denominators that are multiples of 10 to decimals is relatively straightforward. The examples below show this

Common fraction Decimal
 4 10
. 4     .4
 9 10
. 9     .9
 45 100
. 4 5   .45
 56 100
. 5 6   .56
 894 1000
. 8 9 4 .894
 321 1000
. 3 2 1 .321

There are some fractions of this type that are slightly trickier to convert. Understanding decimal place value and using zeros as place holders is required as shown below.

Common fraction Decimal
 6 100
. 0 6   .06
 8 100
. 0 8   .08
 34 1000
. 0 3 4 .034
 4 1000
. 0 0 4 .004

## When the denominator is not a multiple of 10

There are at least two options for converting a fraction to a decimal when the denominator is not 10, 100, or 1000. The first of these is quick and involves dividing the numerator by the denominator as shown below.

The method above will often give a repeating decimal which may need to be rounded. For example, 1/3 (one-third) approximates to 0.333. There is more on rounding decimals here.

Another way to change to decimals is to find an equivalent fraction with a denominator of 10, 100, 1000, and so on. The two examples below show this.

#### Example 1

 4 5 = ? 10 What was the denominator multiplied by to get to 10? It was multiplied by 2. Do the same to the numerator. 4 x 2 = 8 4 5 = 8 10 = 0.8

#### Example 2

 7 20 = ? 100 What was the denominator multiplied by to get to 100? It was multiplied by 5. Do the same to the numerator. 7 x 5 = 35 7 20 = 35 100 = 0.35

Many times there is no equivalent fraction with a multiple of 10 as denominator. In these cases you can approximate the answer by dividing top by bottom.

### Worksheets

Practice changing fractions to decimals using the worksheets above.

You will also find a fraction/ decimal conversion chart here. You can also use this fraction bar/ chart which includes a decimal bar to illustrate and practice the conversion of common fractions to decimals.

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