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Decimal numbers are numbers expressed in the base-10 numeral system using a decimal point to separate the integer part from the fractional part. The notation employs ten digits, 0 through 9, and a place-value structure that assigns increasing powers of ten to digits as they move left or right of the decimal point. A decimal number may be an integer, a finite decimal with a terminating fractional part, or an infinite decimal expansion that may be repeating or non-repeating.

Finite decimals terminate after a finite number of digits, such as 3.14 or 0.5. Infinite decimals may be repeating, like 0.333..., which represents 1/3, or non-repeating, as in the decimal expansion of many irrational numbers such as pi. Decimal notation provides a straightforward representation of many real numbers and underpins common measurements and arithmetic.

Arithmetic with decimal numbers relies on aligning decimal points for addition and subtraction, and tracking the number of fractional digits when performing multiplication or division. A decimal’s precision is determined by how many fractional digits are recorded. In fractions, a finite decimal occurs precisely when the fraction’s reduced denominator has only 2s and 5s as prime factors; all other fractions yield infinite repeating decimals.

In computing, decimal numbers may be represented approximately in binary as floating-point numbers, which can introduce rounding errors. To avoid this in finance and commerce, many languages provide decimal or fixed-point types that preserve exact decimal arithmetic. The concept of decimal numbers has historical roots in the work of Simon Stevin, who popularized decimal fractions in Europe during the late 16th century, contributing to widespread adoption of decimal notation in mathematics and commerce.