Luke Paireepinart wrote: > I've always wondered: > There are numbers in Decimal that can't be represented accurately in > Binary without infinite precision. > But it doesn't go the other way. Rational base-2 numbers are rational > base-10 numbers. I'm supposing this is because base-10 is a higher base > than base-2.
It is because 10 is an exact multiple of 2, not just because it is larger. The place values of a decimal fraction are (1/10)**n. The place values of a binary fraction are (1/2)**n or (5/10)**n. So any binary fraction can be rewritten as a decimal fraction. > So I've wondered that, even though Pi is an irrational number in > base-10, is it possible that it's a simple (rational) number in a higher > base? No. First, rational vs irrational has nothing to do with whether it can be represented in a particular base. 1/7 is rational but has no finite representation as a decimal fraction. pi is a transcendental number which means it is not the solution of any polynomial equation with rational coefficients. In particular, it is not rational. But any number that can be represented as a 'decimal' fraction in any (rational) base is rational so this is not possible with pi. > I mean, I suppose a base of Pi would result in Pi being 1, but what > about integer bases? > Is there some kind of theory that relates to this and why there's not a > higher base with an easy representation of Pi? http://en.wikipedia.org/wiki/Transcendental_numbers Kent _______________________________________________ Tutor maillist - Tutor@python.org http://mail.python.org/mailman/listinfo/tutor
