JT
Posts:
1,448
Registered:
4/7/12


Re: Can a fraction have none noneending and nonerepeating decimal representation?
Posted:
Jul 31, 2013 7:13 PM


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... > > > > Julio
So what is valid for a hexagon is equally valid for a pentagon, it just require some more thought using 15 to get the fraction of the radius. Good to know if you want to use base 10 to get a rational out of Pi.

