# Decimal to fraction conversion

All decimal numbers can be expressed as a fraction. Decimal to fraction conversion is usually a two-step operation.

• First, convert the decimal to fraction using tenths, hundredths, thousandths, etc. depending on the number of decimal places. e.g. 1.75 = 1 75/100.
• Next, simplify the fraction part to the lowest common term. e.g. 75/100 = 3/4.

Fractions and decimals are very similar. In fact, decimal numbers are more correctly known as decimal fractions and fractions with numerators and denominators are, to give them a longer name, common fractions. Help your children to understand that (common) fractions and decimal (fractions) have the same meaning – part of the whole.

## Converting a decimal to a fraction

Decimals are fractions that have powers of ten as their denominators. Or, to say another way, they have 10, 100, 1000, and so on as the bottom number of the fraction.

The main thing when we convert from decimal to common fractions is to find out what we are dealing with. Is it tenths? Is it hundredths? Or is it thousandths?

The examples below show decimals can be shown as common fractions.

We write as a decimal    We read, or say We write as a common fraction
.3 . 3     three tenths
 3 10
.7 . 7     seven tenths
 7 10
.23 . 2 3   twenty-three hundredths
 23 100
.61 . 6 1   sixty-one hundredths
 61 100
.597 . 5 9 7 five hundred ninety-seven thousandths
 597 1000
.439 . 4 3 9 four hundred thirty-nine thousandths
 439 1000

The place value of the number on the right tells whether the common fraction is in tenths, hundredths, thousandths, and so on.

Consider reviewing how place value for tenths, hundredths, and thousandths are used with decimal numbers before working on converting decimal to common fractions.

### Writing the common fraction in simplest form

Common fractions are usually written in simplest form. Sometimes this is also called writing fractions using the lowest terms. You'll find more about how to simplify fractions here.

#### Simplifying fractions: using common factors

To simplify a common fraction we find the greatest common factor for the numerator and the denominator and then use it to divide both. The steps below show an example of how to do this:

What is the fraction?
 64 100
Find the common factors 1 , 2 , 4
Find the greatest common factor 4
Divide 16 (the numerator) by 4 64 ÷ 4 = 16
Divide 20 (the denominator) by 4 100 ÷ 4 = 25
Write the fraction in simplest form
 16 25

If necessary, review the concept of equivalent fractions with your child before working on simplifying common fractions.

The worksheets below will help with changing between fractions and decimals.

You can try this decimals and percentages as fractions game for a little educational fun.

### Working with the chart and worksheets

Practicing converting between decimals and proper fractions with the worksheets and the Equivalents Chart is a good way for your child to reinforce their understanding of the concept.

By Subject > Decimals > Converting to fractions