Look at several examples of rational numbers in the form p/q (q≠0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?

The property that q must satisfy in order that the rational numbers in the form p/q, where p and q are integers with no common factor other than 1, have terminating decimal representation is: the prime factorization of q has only powers of 2 or powers of 5 or both. i.e., 2m × 5n, where m = 1, 2, 3, … and n = 1, 2, 3, …