Re: evolution of bytes, The joy of FORTRAN

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.