Tuesday, August 06, 2013

[udzptivy] Duodecimal fraction expansions

Left hand side is decimal; right hand side is in base 12.

1/2 = 0.6
1/3 = 0.4
2/3 = 0.8
1/4 = 0.3
3/4 = 0.9
1/5 = 0.2497 2497 2497...
2/5 = 0.4972 4972 4972...
3/5 = 0.7249 7249 7249...
4/5 = 0.9724 9724 9724...
1/6 = 0.2
5/6 = 0.A
1/8 = 0.16
3/8 = 0.46
5/8 = 0.76
7/8 = 0.A6
1/9 = 0.14
2/9 = 0.28
4/9 = 0.54
5/9 = 0.68
7/9 = 0.94
8/9 = 0.A8
1/10 = 0.1 2497 2497 2497...
3/10 = 0.3 7249 7249 7249...
7/10 = 0.8 4972 4972 4972...
9/10 = 0.A 9724 9724 9724...
1/12 = 0.1
5/12 = 0.5
7/12 = 0.7
11/12 = 0.B
1/18 = 0.08
5/18 = 0.34
7/18 = 0.48
11/18 = 0.74
13/18 = 0.88
17/18 = 0.B4
1/24 = 0.06
23/24 = 0.B6
1/36 = 0.04
35/36 = 0.B8
1/72 = 0.02
71/72 = 0.BA

Generated by generating a bc script, then a perl script and hand editing the output. Adding 1/10^35 is to avoid ending with BBBBBB (the dozenal equivalent of 999999).

obase=12
scale=40
print "1/2 = "
1/2+1/10^35
...

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