Recurring Decimals

Example:

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. 

  X=7/9

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....

X=0.4545454545

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

-X

99X=45

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