Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Search Thread: Advanced Search

 Messages: [ Previous | Next ]
 Barry Schwarz Posts: 177 Registered: 3/13/08
Re: Terminating Deciamal Expansion
Posted: Jan 19, 2013 2:06 PM
 Plain Text Reply

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)

--
Remove del for email

Date Subject Author
1/18/13 Charles Hottel
1/18/13 Virgil
1/19/13 Charles Hottel
1/19/13 Barry Schwarz

© The Math Forum at NCTM 1994-2018. All Rights Reserved.