Write 0.2(54) as a fraction in its simplest form. (Where 0.2(54) = 0.254545454...)

Let x = 0.2(54) = 0.2545454...

Then 100x = 25.454545... = 25.4(54)

So 99x = 100x - x = 25.4(54) - 0.2(54) = 25.2

Hence 990x =252

Therefore x = 252/990 = 14/55