On Fri, 25 Aug 2017 04:12 pm, Chris Angelico wrote: >> And there are numbers which repeat in decimal but not binary, and numbers >> which repeat in both, and numbers which don't repeat in either. > > Which ones repeat in decimal but not binary? An example, please.
What? No. I never said that, that would be silly. You must be replying to some other Steven. *wink* Quoting Wikipedia: "A rational number has a terminating sequence after the radix point if all the prime factors of the denominator of the fully reduced fractional form are also factors of the base. [...] A rational number has an infinitely repeating sequence of [digits] if the reduced fraction's denominator contains a prime factor that is not a factor of the base." https://en.wikipedia.org/wiki/Repeating_decimal#Extension_to_other_bases Fractions will terminate in decimal if their denominator is a power of two, a power of five, or a multiple of such, e.g.: 2, 4, 8, 16, 32, 64, ... 5, 25, 125, 625, ... 10, 20, 40, 50, 80, 100, ... and will terminate in binary if their denominator is: 2, 4, 8, 16, 32, ... so obviously any number which terminates in binary will also terminate in decimal, but not necessarily vice versa. Fractions will repeat in decimal if their denominator is a multiple of any of the following primes: 3, 7, 11, 13, 17, ... and fractions will repeat in binary if their denominator is a multiple of: 3, 5, 7, 11, 13, 17, ... so clearly any number which repeats in decimal will also repeat in binary. Like I said.[1] How did we get onto prime factors of denominators? The point I was making is that there are plenty of fractions which are not multiples of 1/5 which nevertheless lead to unintuitive "wrong answers" in both Decimal and binary floating point. It is not necessary for the fraction to have a denominator which is a multiple of 5 to run into issues. [1] Just now. What may have been said in the past is the past, and long forgotten. *wink* -- Steve “Cheer up,” they said, “things could be worse.” So I cheered up, and sure enough, things got worse. -- https://mail.python.org/mailman/listinfo/python-list