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positional numeral system
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The number 258,458 expressed in the sexagesimal (base 60) system of the Babylonians and in cuneiform. A chart displays the Mayan numeral system, showing symbols for numbers 0 to 19 using dots and bars, and demonstrates how larger numbers are formed by stacking these symbols vertically in a base-20 system. An example calculation on the right breaks down the number 258,458 using Mayan numerals and powers of 20.
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positional numeral system

mathematics
Also known as: place-value system
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The number 258,458 expressed in the sexagesimal (base 60) system of the Babylonians and in cuneiform.
The number 258,458 expressed in the sexagesimal (base 60) system of the Babylonians and in cuneiform.

A positional numeral system is a method of representing numbers where the value of a digit depends on its position within the number. This is in contrast to older systems where symbols had fixed values regardless of placement.1

In a positional system, each digit's place has a specific "place value," which is typically a power of a base number. For example, in the decimal system (base 10), the number 234 means (2 \times 10^2 + 3 \times 10^1 + 4 \times 10^0). The digits used are from 0 up to one less than the base.12

The development of a symbol for zero was crucial for positional systems to distinguish between numbers like 792 and 7,092. The Hindu-Arabic numeral system, which uses base 10 and includes zero, is the most common positional system used today. Other positional systems include the binary system (base 2) and the hexadecimal system (base 16), which are important in computing.31

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4 Britannica Sources
  1. numeral system
  2. positional notation
  3. numerals and numeral systems - Multiplicative grouping systems
  4. numerals and numeral systems - Positional numeral systems

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