for decimal form a useful fact is
a real nummber x is rational if and only if its decimal expansion at some point repeats.
let () be repeat this sequence
1/9=.(1) so rational
8134808921309.2872918752801(29148991280409) so rational
The question has been answered, but maybe I can help you grasp this a little easier. "Irrational" means that it cannot be expressed as a ratio (NOT that it is 'irrational' in the sense of not being reasonable.) Hence "irrational," or "un-ratio-expressable" if you will. A rational number, on the other hand, CAN be expressed as a ratio. It's "rational," or "ratio-expressable." Since a repeating decimal is given by the 'ratio' of two numbers, it is indeed rational (i.e. 'expressable as a ratio.')