recurring decimal to fraction

How to express recurring decimal number into fraction?

Let us take the example of 34.56565656565…..

Let “x” = 34.5656565656………..                     (1)

Since, 0.56 is recurring, we will multiply by 100. The decimal side will remain unchanged.

So, 100x = 3456.565656……….       (2)

Subtracting (1) from (2), we have

99x = 3422

Or, x = 3422/99 

or x   =  34 56/99 

Answer