On Fri, 18 Jan 2013 22:44:16 -0500, "Charles Hottel" <firstname.lastname@example.org> wrote:
>I would appreciate some hints on solving this problem: > >Show that any rational number p/q, for which the prime factorization of q >consists entirely od 2s and 5s, has a terminating decimal expansion. >Thanks.
Not a nice as Virgil's proof but if you could also use induction in two steps:
If q = 2^m * 5^n and p/q has terminating expansion 1 - show same is true for q = 2^(m+1) * 5^n 2 - show same is true for q = 2^m * 5^(n+1)