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Topic: Can a fraction have none noneending and nonerepeating decimal representation?
Replies: 108   Last Post: Aug 16, 2013 5:22 PM

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 JT Posts: 1,448 Registered: 4/7/12
Re: Can a fraction have none noneending and nonerepeating decimal representation?
Posted: Jul 31, 2013 7:31 PM

Den torsdagen den 1:e augusti 2013 kl. 01:29:54 UTC+2 skrev jonas.t...@gmail.com:
> Den torsdagen den 1:e augusti 2013 kl. 01:16:13 UTC+2 skrev Julio Di Egidio:
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> > <jonas.thornvall@gmail.com> wrote in message
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> > > Den torsdagen den 1:e augusti 2013 kl. 00:51:42 UTC+2 skrev Julio Di
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> > > Egidio:
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> > >> <jonas.thornvall@gmail.com> wrote in message
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> > >>
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> > >> > One question can fractions be expressed using
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> > >> > other bases, and must they necessarly have
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> > >> > ending nonerepeating pattern in base 10.
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> > >> Yes and no.
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> > >> Given *any* integer base > 1 of representation, the fractional expansion
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> > >> of
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> > >> a rational number is *always* periodic (even when the period is just a
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> > >> zero). The opposite for irrational numbers.
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> > >> I am not clear what happens with rational bases, though. For base n/m:
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> > >> fract(x) = Sum_{ i > 0 } [ x_i * (n/m)^(-i) ]
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> > >> and, in general, an m-th root is not rational...
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> > > If that is your answer it seem to me like you say what is rational in one
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> > > base
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> > > is not necessarily a rational in another base.
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> > My answer to your question ends before the "I am not clear" part. The rest
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> > is my own late night ruminations.
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> > > Who could have guessed.
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> > You, of course.
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> > Good night,
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> > Julio
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> The question was if a fraction (rational) expressed in one base, must necessarily have terminating and nonerepeating pattern in another base.
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> And i am pretty sure you answered no to that one, which means that the rational numbers is basedependent.
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> I think i guessed that, or solved it in another continuum, well it could be same 1997.

Well it was the second time, the first time was in a galaxy far far away.

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