Answer :

Let,


x = 0.4233333333….. ….equation 1


As 3 is the repeating term, so in all such problems multiply both sides of the equation with a number such that complete repetitive part of number comes after the decimal.


multiplying equation 1 with 100 in both sides, we have –


100x = 42.3333333333… …equation 2


Subtracting equation 1 from equation 2,we get-


100x – x = 42.3333333… - 0.423333333…


99x = 41.91 {as letter terms gives zero only 42.33-0.42 gives result}


x = 41.91/99


x = 4191/9900


Note: We can also solve these problems using geometric progression, but the above method is much simpler.


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