Express each of the following decimals in the rational form .

let x =

X = 0.575757….. -→(i)

Here the periodicity of the decimal is two

So, we multiply both sides of (i) by 100 and we get

100x = 57.575757…-→(ii)

Subtract (i) from (ii)

100x = 57.5757….

X = 0.5757…

99x = 57.0

(divide by 99 on both sides)

Hence ₌