Decimal

A decimal is a number expressed in the base-10 positional numeral system, where each digit has a place value that depends on its position relative to the decimal point. The decimal point separates the integer part from the fractional part, with digits to the right representing tenths, hundredths, thousandths, and so on.

Decimals are capable of representing both rational and irrational numbers in decimal form. A terminating decimal ends after a finite number of digits (for example, 2.75 or 0.5); a non-terminating decimal continues forever, often with a repeating pattern (such as 0.333... or 0.142857142857...). The decimal representation of a rational number may be terminating or repeating; irrational numbers have non-terminating, non-repeating decimals.

The decimal system uses ten digits 0–9 and is closely tied to the decimal point, a symbol that is rendered as a point or a comma in different locales. The concept of decimal fractions originated in ancient Indian mathematics and was transmitted through the Islamic world to Europe. Simon Stevin's 1585 treatise popularized decimal fractions in Europe. The term decimal derives from the Latin decimus, meaning tenth.

In practice, decimals are widely used in science, engineering, finance, and everyday measurement. Every terminating decimal equals a fraction with a power-of-10 denominator; nonterminating decimals may represent fractions with larger denominators. In computing, decimals are often approximated using fixed- or floating-point representations, which can introduce rounding errors and precision limits.