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.