|
Post by fcg710647 on Dec 6, 2017 16:08:39 GMT -8
Centavigesimal would be an excellent base if it were not very large, as it is adjacent to two composite numbers (119 = 7 * 17 and 121 = 11^2). In other words, sevenths, elevenths, and seventeenths don't have long recurring periods, so in a per-digit sense it is elegant for a lot of fractions.
Ideally, alternating decimal and dozenal would fit centavigesimal well. On the other hand, writing each digit as a decimal number from 0 to 119 and separating them with commas looks like this:
Centavigesimal reciprocals.
1/2 = 0.60
1/3 = 0.40
1/4 = 0.30
1/5 = 0.24
1/6 = 0.20
1/7 = 0.17,17,17,17,17,17,17,....
1/8 = 0.15
1/9 = 0.13,40
1/10 = 0.12
1/11 = 0.10,109,10,109,10,109,10,109,....
1/12 = 0.10
1/13 = 0.9,27,83,9,27,83,9,27,83,9,27,....
1/14 = 0.8,68,68,68,68,68,68,....
1/15 = 0.8
1/16 = 0.7,60
1/17 = 0.7,7,7,7,7,7,7,7,7,....
1/18 = 0.6,80
1/19 = 0.6,37,107,44,25,31,69,56,81,6,37,107,44,25,31,69,56,....
1/20 = 0.6
1/21 = 0.5,85,85,85,85,85,85,85,85,....
1/22 = 0.5,54,65,54,65,54,65,54,65,54,65,...
Thirteen is really not that bad, it is nineteen that brings out the first period longer than three.
|
|