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Change Recurring Decimals into Fractions

In this worksheet, students will change recurring decimals into fractions.

'Change Recurring Decimals into Fractions ' worksheet

Key stage:  KS 3

Year:  Year 9 Maths worksheets

Curriculum topic:   Number

Curriculum subtopic:   Use Relationships Between Operations

Difficulty level:  

Worksheet Overview

In this activity, we are going to convert recurring decimals to fractions!


What we know already!

We know that there are common decimals which can be converted to fractions easily.

For example, 0.5 = 1/2      or     0.2 = 1/5      or       0.25 = 1/4

These are called terminating decimals because they end!


policeman saying stop


What is a decimal called that does not end, and goes on to infinity?  

For example, 0.3333333333333333333...................

This type of decimal is caller a recurring decimal as it does not terminate - it recurs! 

However, we do know that 0.33333333333........... = 1/3 as a fraction.


green tick



There are other recurring decimals which we do not know quite so well, so we need a way to work them out!


Let's take 0.4444444444444 ..... and change it to a fraction!


Answer (using some algebra) Hurrah!

Step 1 - We let the decimal = x

x = 0.444444444444............

(The aim of the game is to get rid of all those 4's)


Step 2 - We multiply through by 10

10x = 4.4444444444444...........


Step 3 - Subtract one from the other

10x = 4.4444444444444...........

    x = 0.4444444444444...........


 9x = 4         


 (That is, 10x - x = 9x      and     4.44444... - 0.44444..... = 4)


Can you see how that gets rid of the recurring decimal?

It looks so much better!


Step 4 - Divide through by the x coefficient to form a fraction.

9x = 4

Divide through by 9

x = 4/9


Are you happy to try some of these now? You can look back at the introduction at any point during the activity by clicking on the red help button on the screen.

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