Let, x = 0.68686868…
⇒ x = 0.68 + 0.0068 + 0.000068 + …∞
⇒ x = 68(0.01 + 0.0001 + …∞)
⇒ x = 68 \(\left(\frac{1}{10^2} + \frac{1}{10^4} + \frac{1}{10^6} + \frac{1}{10^9} + .... \infty\right)\)
Here, a = \(\frac{1}{10^2}\) and r = \(\frac{1}{10^2}\)
\(\Rightarrow\) x = \(\left(68\times \frac{1}{99}\right)\) = \(\frac{68}{999}\)
\(0.\overline{68}\) = \(\frac{68}{999}\)