In the form: .ababa...

A decimal with a two-digit repeating pattern, like $.ababab...$, can be converted to the fraction $\frac{ab}{99}$, where $ab$ represents the two-digit number. This is derived from the infinite geometric series $\frac{ab}{100} + \frac{ab}{10000} + \dots$, which sums to $\frac{ab/100}{1 - 1/100} = \frac{ab}{99}$. For example, $.242424... = \frac{24}{99} = \frac{8}{33}$. This pattern extends to any continuously repeating block of digits; for example, $.abcabc... = \frac{abc}{999}$.