Detecting that a fraction is a repeating decimal

Correct.

From wikipedia:

A decimal representation written with a repeating final 0 is said to terminate before these zeros. Instead of "1.585000…" one simply writes "1.585". The decimal is also called a terminating decimal. Terminating decimals represent rational numbers of the form $k/(2^n5^m)$.

http://en.wikipedia.org/wiki/Repeating_decimals