A little addition to what others already said: in base d you can only represent exactly numbers expressed by fractions a/b with b a divisor of some power of d. In other words, to check if a reduced fraction a/b is expressable in finite form (not periodic) in base d, all prime divisors of b must also divide the base d.

Thus, 13/24 has a finite form in base 6, since 24=2^3*3, and both 2 and 3 are factors of 6, but not in base 10 or 2. 1/2 has a finite form in base 2 and 10, but not 3 and so on.