Express as a fraction in simplest form.

Step-by-step solution

Let x = = a + b …(i) (i) Consider a = = 0.383838 ... 100 a = = 38 + = 38 + a 100 a – a = 38 99 a = 38 a = (ii) Consider b = Multiplying both sides by 10, we get 10 b = Again multiplying both sides by 10, we get 100 b = Now, 100 b – 10 b = – = 115 90 b = 115 b = From (i), we have x = a + b = = x =