Of the eleven fractions 1/2, 1/3, 1/4, …, 1/12, how many have a decimal expansion that terminates?

A fraction in lowest terms terminates exactly when its denominator is built from the primes 2 and 5 only. Running through the denominators 2 to 12, the ones that qualify are 2, 4, 5, 8 and 10, giving 0.5, 0.25, 0.2, 0.125 and 0.1 — five of them. The remaining six denominators (3, 6, 7, 9, 11, 12) each carry a 3, 7 or 11, so those fractions recur. Counting 12 as well because it looks "even enough" is the usual slip: $12=2^2\times 3$, and the stray 3 makes 1/12 = 0.08333… recur.