Base 30 or trigesimal is a positional numeral system

Positional notation

Positional notation or place-value notation is a method of representing or encoding numbers. Positional notation is distinguished from other notations for its use of the same symbol for the different orders of magnitude...

 using 30

30 (number)

30 is the natural number following 29 and preceding 31.-In mathematics:30 is the sum of the first four squares, which makes it a square pyramidal number.It is a primorial and is the smallest Giuga number....

 as the radix

Radix

In mathematical numeral systems, the base or radix for the simplest case is the number of unique digits, including zero, that a positional numeral system uses to represent numbers. For example, for the decimal system the radix is ten, because it uses the ten digits from 0 through 9.In any numeral...

. Digits in this base can be represented using the Arabic numerals

Arabic numerals

Arabic numerals or Hindu numerals or Hindu-Arabic numerals or Indo-Arabic numerals are the ten digits . They are descended from the Hindu-Arabic numeral system developed by Indian mathematicians, in which a sequence of digits such as "975" is read as a numeral...

 0-9 and the Latin letters

Latin alphabet

The Latin alphabet, also called the Roman alphabet, is the most recognized alphabet used in the world today. It evolved from a western variety of the Greek alphabet called the Cumaean alphabet, which was adopted and modified by the Etruscans who ruled early Rome...

 A-T.

From a mathematical viewpoint, 30 is a convenient choice for a base in that it is the 4th primorial

Primorial

In mathematics, and more particularly in number theory, primorial is a function from natural numbers to natural numbers similar to the factorial function, but rather than multiplying successive positive integers, only successive prime numbers are multiplied...

 number; many vulgar fractions are easily expressed in base 30. On the other hand, base 30 has poor radix economy

Radix economy

Various proposals have been made to quantify the relative costs between using different radices in representing numbers, especially in computer systems.-Definition:...

, and it shares the problem with base 60 of its radix falling between twin prime

Twin prime

A twin prime is a prime number that differs from another prime number by two. Except for the pair , this is the smallest possible difference between two primes. Some examples of twin prime pairs are , , , , and...

s, 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

Prime factors of the base: 2, 5	Base 30<>b> Prime factors of the base: 2, 3, 5
Fraction	Prime factors of the denominator	Positional representation	Positional representation	Prime factors of the denominator	Fraction
1/2	2	0.5	0.F	2	1/2
1/3	3	0.3333... = 0.	0.A	3	1/3
1/4	2	0.25	0.7F	2	1/4
1/5	5	0.2	0.6	5	1/5
1/6	2, 3	0.1	0.5	2, 3	1/6
1/7	7	0.	0.	7	1/7
1/8	2	0.125	0.3MF	2	1/8
1/9	3	0.	0.3A	3	1/9
1/10	2, 5	0.1	0.3	2, 5	1/A
1/11	11	0.	0.	B	1/B
1/12	2, 3	0.08	0.2F	2, 3	1/C
1/13	13	0.	0.	D	1/D
1/14	2, 7	0.0	0.2	2, 7	1/E
1/15	3, 5	0.0	0.2	3, 5	1/F
1/16	2	0.0625	0.1Q7F	2	1/G
1/17	17	0.	0.	H	1/H
1/18	2, 3	0.0	0.1K	2, 3	1/I
1/19	19	0.	0.	J	1/J
1/20	2, 5	0.05	0.1F	2, 5	1/K
1/21	3, 7	0.	0.1	3, 7	1/L
1/22	2, 11	0.0	0.1	2, B	1/M
1/23	23	0.	0.	N	1/N
1/24	2, 3	0.041	0.17F	2, 3	1/O
1/25	5	0.04	0.16	5	1/P
1/26	2, 13	0.0	0.1	2, D	1/Q
1/27	3	0.	0.13A	3	1/R
1/28	2, 7	0.03	0.12	2, 7	1/S
1/29	29	0.	0.	T	1/T
1/30	2, 3, 5	0.0	0.1	2, 3, 5	1/10