Question 110309
I'm going to assume you have some concept of series. If not, repost maybe and someone else will answer. But .868686868686... is 86(10^(-2)) + 86(10(-4) + 86 (10(-6))...86(10^(-2n)). So it's a 86 times the sum from k=1 to infitnity of 10^(-2k), which converges to 1/99, so it is 86/99.