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

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Barry Schwarz

Posts: 119
Registered: 3/13/08
Re: Terminating Deciamal Expansion
Posted: Jan 19, 2013 2:06 PM
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On Fri, 18 Jan 2013 22:44:16 -0500, "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.

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)

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