19. (See exercise 5.) Explain why it is the case that if a number is rational, its decimal expansion either terminates or, after a certain number of digits, ends with an infinite repeating cluster of digits such as 12:12536. Specifically, explain that if this rational number is given by n m where n and m have no common divisors, then the decimal expansion will terminate by the mth decimal digit, or there will be repeating cluster that will begin on or before the mth decimal digit, and in this case, the repeating cluster can contain at most m  1 digits. (Hint: Think about the remainders you get at each division step.)