Re: evolution of bytes, The joy of FORTRAN

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.