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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 7:29 PM

Den torsdagen den 1:e augusti 2013 kl. 01:16:13 UTC+2 skrev Julio Di Egidio:
> <jonas.thornvall@gmail.com> wrote in message
>
>

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

> > Who could have guessed.
>
>
>
> You, of course.
>
>
>
> Good night,
>
>
>
> Julio

The question was if a fraction (rational) expressed in one base, must necessarily have terminating and nonerepeating pattern in another base.

And i am pretty sure you answered no to that one, which means that the rational numbers is basedependent.

I think i guessed that, or solved it in another continuum, well it could be same 1997.

Date Subject Author
7/30/13 JT
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