express recurring decimal number into fraction (2)

How to express recurring decimal number into fraction?

Let us take the example of 0.534534534…..

Let “x” = 0.534534534………..        (1)

Since, 0.534 is recurring, we will multiply by 1000. The decimal side will remain unchanged.

So, 1000x = 534.534534534……….                (2)

Subtracting (1) from (2), we have

999x = 534

Or, x = 534/999 

 Answer