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From: Pancho <Pancho.Jones@protonmail.com>
Newsgroups: alt.folklore.computers,comp.os.linux.misc
Subject: Re: evolution of bytes, The joy of FORTRAN
Date: Tue, 4 Mar 2025 00:16:03 +0000
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On 3/3/25 23:41, Lawrence D'Oliveiro wrote:
> On Mon, 3 Mar 2025 06:54:31 -0700, Peter Flass wrote:
> 
>> Some fractions that are exact in decimal are only approximate in binary.
> 
> Base-ten has two prime divisors: 2 and 5. Base-two has only 2. So any
> fraction that has a denominator that is the product of any integer powers
> of those divisors can be represented exactly, while others cannot.
> 
> The need to represent 1/3 exactly is also quite common. That’s why I think
> the smallest place-system base that can cope with a reasonable range of
> fractions is 30 -- it has 2, 3 and 5 as prime divisors, and so can cope
> with fraction denominators made up arbitrary products and integer powers
> of all of those.

If you need to represent rational numbers exactly, why not represent 
them as a pair of integers? I find the idea that 1/3 needs to be exact, 
but 1/7 doesn't, contrived.