Positional notation

Positional notation, also known as place-value notation, is the property of a numeral system that the value represented by each symbol in a written numeral depends not only on its appearance but also on its position. Each symbol fits in a specific place or position, representing a power of a fixed base. The most common numeral system used today, the Hindu–Arabic numeral system, is a positional system in base ten; each of ten numerical digits is a distinct symbol representing one of the numbers zero through nine, and in the context of the full numeral, each symbol's value is the digit multiplied by a power of ten.

Most early numeral systems, such as Roman numerals, are essentially based on the additive principle: each symbol type represents one fixed value, and the value of a numeral is the sum of the values of the separate symbols. For example, the Roman numeral CCXXVIII has two copies of the symbol C meaning 100, two copies of X meaning 10, one V meaning 5, and three copies of I meaning 1, so overall represents the number 100 + 100 + 10 + 10 + 5 + 1 + 1 + 1 = 228; by comparison, the equivalent Hindu–Arabic numeral, 228, consists of the symbol 2 representing 2 × 100, another symbol 2 representing 2 × 10, and finally an 8 representing 8 × 1.

The 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. The Inca used knots tied in a decimal positional system to store numbers and other values in quipu cords.

The binary numeral system (base two) is used in almost all computers and electronic devices because it is easier to implement efficiently in electronic circuits.

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