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From: Lawrence D'Oliveiro <ldo@nz.invalid>
Newsgroups: alt.folklore.computers,comp.os.linux.misc
Subject: Re: evolution of bytes, The joy of FORTRAN
Date: Mon, 3 Mar 2025 23:41:46 -0000 (UTC)
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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.