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




Re: Terminating Deciamal Expansion
Posted:
Jan 19, 2013 2:06 PM


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. >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)
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