# The Dozenal System: Part Two- Why 12?

In this part of my blog series on the dozenal system, I will talk about the advantages that the dozenal system has over the decimal system. Before reading this I suggest reading the last part of the series here.

In our day to day life, we only use numbers to do 4 simple things. Add, subtract, multiply and divide. The decimal system works very well for adding and subtracting, as does every other number system and does okay at multiplying, like many other number systems. Its weakness is dividing For example 1/3 = 0.333… repeating for an infinite number of digits. Another example is 1/4 = 0.25. That these two dividends are not nicer and shorter numbers, has an effect on how easy they are to use, when 3 and 4 are so common in day to day life.

The reason decimal fails on the numbers 3 and 4 are because of factors. The number 10 only has the factors 2 and 5 (excluding one and itself). To avoid this issue, we should make the base of our system something with lots of factors like 60 (2, 3, 4, 5, 6, 10, 12, 15, 20 and 30), a so-called super-composite number.

The issue with this is that we would have to create 50 new characters, to represent the number from 10-59, and memorizing them would be more of a hassle than the benefits it provides. This is why people have chosen 12, it is the smallest super composite number, with the factors 2, 3, 4 and 6 and it means we only have to make 2 new characters, for 10 and 11.

The new characters for 10 and 11 are currently non-Unicode type-able, so I will be using the character X and E, as they look like them the most. The character for 10, X is pronounced “dek” as in deca and the character for 11, E is pronounced “el” short for eleven. Dek and El (c) John J. G. Savard, CC BY 4.0

Now division becomes more simple, as 1/3 is written 0.4, 1/4 is written 0.3, 1/6 is written 0.2, 1/2 is written 0.6, 5/6 is written 0.X and 11/12 is written 0.E. This only complicates 1/5, which is written in dozenal as 0. 2497. Overall, the dozenal system would drastically simplify division, be similar in addition and subtraction and very similar in multiplication.

In the next parts of my blog series on the dozenal system, I will talk about pronouncing dozenal numbers, hand counting in the dozenal system, and how we almost ended up using it.