What kinds of denominators generate repeating decimals?

There are specific values of denominators that would yield a non-terminating decimal expansion. In other words, the decimal would be repeating. These denominators are multiples of 3. That could be 3, 6, 9, 12, 15, 18, 21, and so on and so forth.  For example, 1/3 = 0.333333, 1/6 = 0.166666, 1/9 = 0.1111, and so on and so forth.