Editing Positional notation (section)

{{Short description|Method for representing or encoding numbers}}{{Redirects|Positional system|the voting rule|positional voting}}[[File:Positional notation glossary-en.svg|thumb|300px|Glossary of terms used in the positional numeral systems]]
{{numeral systems}}

'''Positional notation''', also known as '''place-value notation''', '''positional numeral system''', or simply '''place value''', usually denotes the extension to any [[radix|base]] of the [[Hindu–Arabic numeral system]] (or [[decimal|decimal system]]). More generally, a positional system is a [[numeral system]] in which the contribution of a digit to the value of a number is the value of the digit multiplied by a factor determined by the position of the digit. In early [[numeral system]]s, such as [[Roman numerals]], a digit has only one value: I means one, X means ten and C a hundred (however, the values may be modified when combined). In modern positional systems, such as the [[decimal|decimal system]], the position of the digit means that its value must be multiplied by some value: in 555, the three identical symbols represent five hundreds, five tens, and five units, respectively, due to their different positions in the digit string.

The [[Babylonian Numerals|Babylonian numeral system]], base 60, was the first positional system to be developed, and its influence is present today in the way time and angles are counted in tallies related to 60, such as 60 minutes in an hour and 360 degrees in a circle. Today, the Hindu–Arabic numeral system ([[base ten]]) is the most commonly used system globally. However, the [[binary numeral system]] (base two) is used in almost all [[computer]]s and [[electronic device]]s because it is easier to implement efficiently in [[electronic circuit]]s.

Systems with negative base, [[complex number|complex]] base or negative digits have been described. Most of them do not require a minus sign for designating negative numbers.

The use of a [[radix point]] (decimal point in base ten), extends to include [[fraction (mathematics)|fractions]] and allows the representation of any [[real number]] with arbitrary accuracy. With positional notation, [[arithmetic|arithmetical computations]] are much simpler than with any older numeral system; this led to the rapid spread of the notation when it was introduced in western Europe.