There are many different numeral systems, that is,

writing system A writing system comprises a set of symbols, called a ''script'', as well as the rules by which the script represents a particular language. The earliest writing appeared during the late 4th millennium BC. Throughout history, each independen ...

s for expressing numbers.

By culture / time period

"A ''base'' is a natural number B whose ''powers'' (B multiplied by itself some number of times) are specially designated within a numerical system." The term is not equivalent to radix, as it applies to all numerical notation systems (not just positional ones with a radix) and most systems of spoken numbers. Some systems have two bases, a smaller (subbase) and a larger (base); an example is Roman numerals, which are organized by fives (V=5, L=50, D=500, the subbase) and tens (X=10, C=100, M=1,000, the base).

By type of notation

Numeral systems are classified here as to whether they use positional notation (also known as place-value notation), and further categorized by radix or base.

Standard positional numeral systems

The common names are derived somewhat arbitrarily from a mix of

Latin Latin ( or ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken by the Latins (Italic tribe), Latins in Latium (now known as Lazio), the lower Tiber area aroun ...

and Greek, in some cases including roots from both languages within a single name. There have been some proposals for standardisation.Multiplication Tables of Various Bases
p. 45, Michael Thomas de Vlieger, Dozenal Society of America

Non-standard positional numeral systems

Bijective numeration

Signed-digit representation

Complex bases

Non-integer bases

''n''-adic number

Mixed radix

* Factorial number system * Even double factorial number system * Odd double factorial number system * Primorial number system * Fibonorial number system * in timekeeping * in timekeeping * (12, 20) traditional English monetary system (£sd) * (20, 18, 13) Maya timekeeping

Other

* Quote notation * Redundant binary representation * Hereditary base-n notation * Asymmetric numeral systems optimized for non-uniform probability distribution of symbols * Combinatorial number system

Non-positional notation

All known numeral systems developed before the Babylonian numerals are non-positional, as are many developed later, such as the

Roman numerals Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, eac ...

. The French Cistercian monks created their own numeral system.

References

{{Reflist Systems Numeral