We have discussed in class the following theorem. A decimal represents a rational number if and only if it is either terminating
(finite, e.g. 0.25) or periodic (repeating, e.g. 0.121212...). Which fractions a/b are represented by terminating
decimals? That is, what is a necessary and sufficient condition on a and/or b in order for the decimal representation
of a/b to be terminating? (Think, for example, about some fractions for a few different values of a and
b: 1/2, 1/3, 3/4, 2/5, 5/6, 2/7, 5/8, 4/9, 7/10, etc. Which of these have a terminating decimal representation and which have
an infinite periodic decimal representation? Now generalize. Prove your claim.)