Virgil
Posts:
8,833
Registered:
1/6/11


Re: Terminating Deciamal Expansion
Posted:
Jan 18, 2013 11:47 PM


In article <1oCdneKuT4nqi2fNnZ2dnUVZ_rCdnZ2d@earthlink.com>, "Charles Hottel" <chottel@earthlink.net> 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.
If q = 2^m*5^n for nonnegative integers m and n, let k = max(m,n)
then r = (p/q)*10^k is an integer, so and p/q = r/10^k. 

