JT
Posts:
1,434
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 > > 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
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.

