Recurring Decimals

Finding the equivilant fraction to a reccuring decimal. This is and A/A* grade topic seen on higher papers at GCSE.

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method of Reccuring Decimals


Prove that 0.7r=7/9

lets say X=0.7777....  

times both sides by 10.  So, 10X=7.77777.

take-a-way 1 of the X from both sides (X=0.777777...)  =   9X=7

Now make X on It's own. 


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Tips and example

If the Decimal has two recurring numbers then instead of timesing both sides by 10 you times it by 100, if it has three recurring numbers then times it by 1000 etc. For example, The answer to the question ' Find the fraction that is equivilant to 0.45r' is 5/11. This is Because....


100X=45.45454545 (remember this is two recurring numbers.)



X=45/99 which is cancelled down to X=5/11

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Two good examples of changing recurring decimals to fractions

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