Dozenal 101

Review of Place Value

In everyday numbers, 12,345.67 means 10,000 + 2,000 + 300 + 40 + 5 + 0.6 + 0.07, or 1*(10^4) + 2*(10^3) + 3*(10^2) + 4*(10^1) + 5*(10^0)  (anything to the zero is equal to 1) + 6/(10^1) + 7/(10^2). This system is called decimal.

Dozenal

However, in the dozenal system, 12345;67 (the semicolon is like the dot in decimal) means 1*(12^4) + 2*(12^3) + 3*(12^2) + 4*(12^1) + 5*(12^0) + 6/(12^1) + 7/(12^2)

Because of this, you need 2 extra digits to represent 10 and 11. Those digits are:

10 - X
11 - Ɛ

Why Use Dozenal?

The dozenal system has many advantages over the decimal system.

You know how fractions like 1/3, 1/6, and 1/12 repeat (0.333333..., 0.166666..., and 0.083333... respectively)? This does not happen in the dozenal system. 1/3 (4/12 or 0;4), 1/6 (2/12 or 0;2), and 1/12 (1/12 or 0;1) are exact values. Since numbers with factors of 3 are more commonly used than factors of 5, There will be seemingly less repeating fractions. Ninths look nicer too (1/12 + 4/144, or 0;14).

Quarters, Eights, and Sixteenths (or Dozen-fourths if you are using dozenal) also look nicer (0;3, 0;16, and 0;09 vs 0.25, 0.125, and 0.0625 respectively). This is because 12 has two factors of 2, while 10 only has one.