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Fractions, Dozenals and Irrational Numbers
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Here are some dozenal fractions, dozenals (uncials) and irrational numbers.

Note: Iā€™m using Ī› for ten and ʐ 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.(186Ī›35), 2/7 = 0.(35186Ī›), 3/7 = 0.(5186Ī›3), 4/7 = 0.(6Ī›3518), 5/7 = 0.(86Ī›351), 6/7 = 0.(Ī›35186)

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.Ī›6

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.Ī›8

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/ʐ = 0.(1), 2/ʐ = 0.(2), 3/ʐ = 0.(3), 4/ʐ = 0.(4), 5/ʐ = 0.(5), 6/ʐ = 0.(6), 7/ʐ = 0.(7), 8/ʐ = 0.(8), 9/ʐ = 0.(9), Ī›/ʐ = 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›, ʐ/10 = 0.ʐ

āˆš2 = 1.4ʐ79170Ī›07ʐ85737704ʐ085486853...

Ļ€ = 3.184809493ʐ918664573Ī›6211ʐʐ151...

Ļ„ = 6.349416967ʐ635108ʐ2790423ʐĪ›2Ī›2...

e = 2.8752360698219ʐĪ›71971009ʐ388Ī›Ī›...

One thing to note is that the nice pattern 18281828 at the beginning of e is no longer present in dozenal.

Ļ• = 1.74ʐʐ6772802Ī›46Ī›6Ī›186530714908...

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