Nonary

Nonary /ˈnɒnəri/, also known as nonal, is a numeral system with nine as its base. It's mainly known for being a compact notation for ternary (base 3), where each digit symbolizes two trits (ternary digits).

Comparison between ternary and nonary

ternary	nonary
00	0
01	1
02	2
10	3
11	4
12	5
20	6
21	7
22	8

Fun facts and comparisons to other bases

Nonary serves as a compact notation for ternary, using the same digits as in decimal with the exclusion of 9. It is seen as a convenient compaction method due to the similarities between it and decimal (10₉ = 9₁₀, 11₉ = 10₁₀, etc. until 18₉ = 17₁₀). Nonary itself is also related to septemvigesimal (base 27), in which the digits range from 0-9 and the letters A-Q (Q₂₇ = 28₉ = 222₃ = 26₁₀). The only prime factor of nine is three, so only powers of three can be represented as decimals that are not recurring. Every non-recurring decimal is turned into a recurring decimal just by appending an infinite string of eights (the highest digit before 10₉).

Fractions in nonary

fraction (nonary)	nonary decimal extension	decimal equivalent
1⁄2	0.4	0.5
1⁄3	0.3	0.3
1⁄4	0.2	0.25
1⁄5	0.17	0.2
1⁄6	0.14	0.16
1⁄7	0.125	0.142857
1⁄8	0.1	0.125
1⁄109	0.1	0.1
1⁄119	0.08	0.1

Multiplication table

A nonary multiplication table

×	1	2	3	4	5	6	7	8	10
1	1	2	3	4	5	6	7	8	10
2	2	4	6	8	11	13	15	17	20
3	3	6	10	13	16	20	23	26	30
4	4	8	13	17	22	26	31	35	40
5	5	11	16	22	27	33	38	44	50
6	6	13	20	26	33	40	46	53	60
7	7	15	23	31	38	46	54	62	70
8	8	17	26	35	44	53	62	71	80
10	10	20	30	40	50	60	70	80	100