Duodecimal

The duodecimal system (also known as base-12 or dozenal) is a base twelve number system. This means that it has 12 digits to represent numbers, instead of the 10 that decimal uses. In other words, it can represent numbers from zero to eleven with just one digit.

Twelve has more factors than any smaller number. As a result, duodecimal is considered better than decimal with fractions. Duodecimal can handle halves, thirds, quarters, and sixths with very simple fractions. Decimal only has very simple fractions for halves and fifths.

How to represent 10 and 11 in duodecimal

There are no numerical symbols that represent 10 and 11 in duodecimal, so letters taken from the English alphabet are used, specifically X (from the Roman numeral for ten) and E (from the initial of eleven). Some people use A and B (as ann and bet) as well.^[1]

Edna Kramer in her 1951 book The Main Stream of Mathematics used * and # for 10 and 11. The symbols were chosen because they are available in typewriters and push-button telephones.^[1]

This article uses ↊ (dec) and ↋ (elf) for 10 and 11.

Duodecimal values

Decimal	Duodecimal
0	0
1	1
2	2
3	3
4	4
5	5
6	6
7	7
8	8
9	9
10	↊
11	↋
12	10
13	11
23	1↋
24	20
25	21
50	42
60	50
100	84
140	↋8
500	358
720	500
1000	6↋4
1727	↋↋↋
1728	1000

fraction (decimal)	Decimal	duodecimal
1/2	0.5	0;6
1/3	0.3	0;4
2/3	0.6	0;8
1/4	0.25	0;3
1/5	0.2	0;2497
1/6	0.16	0;2
1/7	0.142857	0;186↊35
1/8	0.125	0;16
1/9	0.1	0;14
1/10	0.1	0;12497
1/11	0.09	0;1
1/12	0.083	0;1
1/13	0.0769230	0;0↋
1/24	0.0416	0;06
1/144	0.00694	0;01