LudovicoVan
Posts:
4,033
From:
London
Registered:
2/8/08


Re: Can a fraction have none noneending and nonerepeating decimal representation?
Posted:
Jul 31, 2013 7:16 PM


<jonas.thornvall@gmail.com> wrote in message news:560f0643109045cab19fc7b3f292bc9f@googlegroups.com... > Den torsdagen den 1:e augusti 2013 kl. 00:51:42 UTC+2 skrev Julio Di > Egidio: >> <jonas.thornvall@gmail.com> wrote in message >> news:150fdc29c0f4471283a717c38f8ce257@googlegroups.com... >> >> > 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 mth 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

