On 06/05/2010 11:29 AM, Luke-Jr wrote:
On Saturday 05 June 2010 09:33:03 am Otto Stolz wrote:
In the decimal systems, you can easier divide by 2, 5,
and powers of 10, whilst in the hexadekadic system,
you can easier divide by many powers of two, and all
powers of 16.
And 4, and 8. Many repeating fractions also become more accurate with base 16.
This makes no sense whatsoever. How can a repeating fraction become
"more accurate"? I suppose this means that the accuracy is higher for
given number of digits after the radix point. But that's true just
because 16 is greater than 10, and we could do better still with base 24
or base 30.
In point of fact, the divisibility of 16 is pretty lousy, and only
fractions with denominators that are powers of two can be represented as
terminating "decimals." Base ten can handle powers of 2 and 5 (to be
sure, requiring a few more places before terminating for 4 and 8, etc).
Base 12 is better still, since it brings in 3, and there's a good
argument to be made that thirds are more useful in ordinary life than
fifths. (This is really the only advantage to base 12, and it's why I
joined the Dozenal Society: to see how they could somehow write
newsletters and such around only one valid point).
You may wonder, why I am using the term “hexadekadic”.
This is because, “hexadeka” is the Greek word for 16,
whilst the Latin word ist “sedecim”; there is no language
known that has “hexadecim”, or anything alike, for 16.
There are a bunch of words in English that have such hybrid derivations.
We live with it.
~mark
