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Topic: Terminating Deciamal Expansion
Replies: 3   Last Post: Jan 19, 2013 2:06 PM

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Virgil

Posts: 9,012
Registered: 1/6/11
Re: Terminating Deciamal Expansion
Posted: Jan 18, 2013 11:47 PM
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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 non-negative 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.
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