Base 30 - The Encyclopedia

From Wikipedia, the free encyclopedia.

Numeral systems by culture
Hindu-Arabic numerals
Western Arabic Eastern Arabic Khmer	Indian family Brahmi Thai
East Asian numerals
Chinese Suzhou Counting rods	Japanese Korean Mongolian
Alphabetic numerals
Abjad Armenian Cyrillic Ge'ez	Hebrew Greek (Ionian) Āryabhaṭa
Other systems
Attic Babylonian Egyptian English	Etruscan Mayan Roman Urnfield
List of numeral system topics
Positional systems by base
Decimal (10)
2, 4, 8, 16, 32, 64
1, 3, 9, 12, 20, 24, 30, 36, 60, more…
v • d • e

Base 30 or trigesimal is a positional numeral system using 30 as the radix. Digits in this base can be represented using the Arabic numerals 0-9 and the Latin letters A-T.

From a mathematical viewpoint, 30 is a convenient choice for a base in that it is divisible by the three smallest prime numbers (2, 3, and 5) and by their multiples 6, 10, and 15 — many vulgar fractions are easily expressed in base 30. On the other hand, base 30 has poor radix economy, and it shares the problem with base 60 of its radix falling between twin primes, resulting in few recurring fractions having short periods.

**Conversion table**
Decimal	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Base 30	0	1	2	3	4	5	6	7	8	9	A	B	C	D	E
Decimal	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29
Base 30	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T

**Fractions in base 30**
Fraction	Base 30
1/2	0.F
1/3	0.A
1/4	0.7F
1/5	0.6
1/6	0.5
1/7	0.48H
1/8	0.3MF
1/9	0.3A
1/10	0.3
1/11	0.2LOGAR85DJ
1/12	0.2F
1/13	0.296RKN
1/14	0.248H
1/15	0.2
1/16	0.1Q7F
1/17	0.1MS7
1/18	0.1K
1/19	0.1HB
1/20	0.1F
1/21	0.1CPL
1/22	0.1AR85DJ2LOG
1/23	0.193RBM56FJGSKQ2I7ONEAD
1/24	0.17F
1/25	0.16
1/26	0.14IDPBG
1/27	0.13A
1/28	0.1248H
1/29	0.1
1/30	0.1

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