Fractions to decimals using equivalent fractions

There are many ways to change fractions to decimals. On this factsheet you will find out how to use equivalent fractions to help you make the conversion.

Example:
What is expressed as a decimal?

The key here is to remember that the decimal system is based on 10s, 100s, 1 000s etc. You can see this if you remind yourself of the column headings with place value:

To change to a decimal you have to turn it into a fraction which has 10, 100 or 1 000 etc. on the bottom.

To do this use your knowledge of equivalent fractions
      = ?

You have to multiply the bottom number by 2 to change it to 10.
Now do the same to the top number (this way the fraction's value does not change).
     2 x 2 = 4
     So =

Now use the column headings to write this fraction as a decimal:

A four in the tenths column is exactly the same as .

You have worked out that is the same as 0.4

Remember: Just take any fraction and find an equivalent fraction with 10, 100, 1 000 etc. on the bottom. This new fraction can easily be written as a decimal.