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Here are some dozenal fractions, dozenals (uncials) and irrational numbers.
Note: Iām using Ī for ten and Ę for eleven. Note: Parentheses mean a repeating dozenal.
1/2 = 0.6
1/3 = 0.4, 2/3 = 0.8
1/4 = 0.3, 2/4 or 1/2 = 0.6, 3/4 = 0.9
1/5 = 0.(2497), 2/5 = 0.(4972), 3/5 = 0.(7249), 4/5 = 0.(9724)
Notice the fifths cycle through the 4 numbers just like sevenths do in base ten. The cycle starts with the smaller number (2) and ends with the bigger number (9).
1/6 = 0.2, 2/6 or 1/3 = 0.4, 3/6 or 1/2 = 0.6, 4/6 or 2/3 = 0.8, 5/6 = 0.Ī
1/7 = 0.(186Ī35), 2/7 = 0.(35186Ī), 3/7 = 0.(5186Ī3), 4/7 = 0.(6Ī3518), 5/7 = 0.(86Ī351), 6/7 = 0.(Ī35186)
The sevenths act the same way as the fifths do but the cycle is longer.
1/8 = 0.16, 2/8 or 1/4 = 0.3, 3/8 = 0.46, 4/8 or 1/2 = 0.6, 5/8 = 0.76, 6/8 or 3/4 = 0.9, 7/8 = 0.Ī6
1/9 = 0.14, 2/9 = 0.28, 3/9 or 1/3 = 0.4, 4/9 = 0.54, 5/9 = 0.68, 6/9 or 2/3 = 0.8, 7/9 = 0.94, 8/9 = 0.Ī8
1/Ī = 0.1(2497), 2/Ī or 1/5 = 0.(2497), 3/Ī = 0.3(7249), 4/Ī or 2/5 = 0.(4972), 5/Ī or 1/2 = 0.6, 6/Ī or 3/5 = 0.(7249), 7/Ī = 0.8(4972), 8/Ī or 4/5 = 0.(9724), 9/Ī = 0.Ī(9724)
The cycle is split when we look at the tenths but the only thing to remember is that tenths are just fifths split into half.
1/Ę = 0.(1), 2/Ę = 0.(2), 3/Ę = 0.(3), 4/Ę = 0.(4), 5/Ę = 0.(5), 6/Ę = 0.(6), 7/Ę = 0.(7), 8/Ę = 0.(8), 9/Ę = 0.(9), Ī/Ę = 0.(Ī),
Elevenths work the same way as ninths do in base ten.
1/10 = 0.1, 2/10 or 1/6 = 0.2, 3/10 or 1/4 = 0.3, 4/10 or 1/3 = 0.4, 5/10 = 0.5, 6/10 or 1/2 = 0.6, 7/10 = 0.7, 8/10 or 2/3 = 0.8, 9/10 or 3/4 = 0.9, Ī/10 or 5/6 = 0.Ī, Ę/10 = 0.Ę
ā2 = 1.4Ę79170Ī07Ę85737704Ę085486853...
Ļ = 3.184809493Ę918664573Ī6211ĘĘ151...
Ļ = 6.349416967Ę635108Ę2790423ĘĪ2Ī2...
e = 2.8752360698219ĘĪ71971009Ę388ĪĪ...
One thing to note is that the nice pattern 18281828 at the beginning of e is no longer present in dozenal.
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