Re: evolution of bytes, The joy of FORTRAN

On Mon, 3 Mar 2025 23:11:09 -0500, c186282 wrote:

On 3/3/25 7:36 PM, Peter Flass wrote:

Lawrence D'Oliveiro <ldo@nz.invalid> 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.
>
>

60 is nice

 
   The Babylonian number system was base-60 ....
 
   Maybe they knew something ?   :-)

I had a very brief career as a math and science teacher.  The curriculum
said I had to teach the kids about base-60. The school used homogeneous
grouping with the A, B, C, and D groups. A few of the A kids enjoyed
playing with the concept. The D kids couldn't make change in base-10 but
the syllabus was the syllabus.