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Place value of number in decimal system. The decimal numeral system (also called the base-ten positional numeral system and denary / ˈ d iː n ər i / [1] or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (decimal fractions) of the Hindu–Arabic numeral system.
For example, "11" represents the number eleven in the decimal or base-10 numeral system (today, the most common system globally), the number three in the binary or base-2 numeral system (used in modern computers), and the number two in the unary numeral system (used in tallying scores). The number the numeral represents is called its value.
Decimal: The standard Hindu–Arabic numeral system using base ten. Binary: The base-two numeral system used by computers, with digits 0 and 1. Ternary: The base-three numeral system with 0, 1, and 2 as digits. Quaternary: The base-four numeral system with 0, 1, 2, and 3 as digits.
An example of a numeral system is the predominantly used Indo-Arabic numeral system (0 to 9), which uses a decimal positional notation. [3] Other numeral systems include the Kaktovik system (often used in the Eskimo-Aleut languages of Alaska, Canada, and Greenland), and is a vigesimal positional notation system. [4]
A real number can be expressed by a finite number of decimal digits only if it is rational and its fractional part has a denominator whose prime factors are 2 or 5 or both, because these are the prime factors of 10, the base of the decimal system. Thus, for example, one half is 0.5, one fifth is 0.2, one-tenth is 0.1, and one fiftieth is 0.02.
The following list includes a decimal expansion and set containing each number, ordered by year of discovery. The column headings may be clicked to sort the table alphabetically, by decimal value, or by set. Explanations of the symbols in the right hand column can be found by clicking on them.