decimalen

Decimalen, or decimals, are numbers expressed in decimal notation, a base-10 system that uses a decimal separator to distinguish the integer part from the fractional part. In many European countries the separator is a comma, while in English-speaking contexts a period is used; both serve the same purpose.

Each finite decimal corresponds to a fraction with denominator a power of ten. For example, 0.75 equals 75/100 or 3/4. Some fractions yield repeating decimals, such as 0.333... for 1/3 or 0.1666... for 1/6. The decimal expansion of a rational number either terminates or repeats; irrational numbers have non-repeating, non-terminating decimals.

Decimals are the basis of many computations and measurements. Arithmetic with decimals requires aligning the decimal points; results are often rounded to a given number of decimal places, depending on the required precision or significant figures.

Conversions between decimals and fractions are straightforward in principle. A decimal with k digits after the separator equals an integer divided by 10^k; conversely, a fraction can be converted to a decimal by division or by factoring the denominator. Some fractions yield terminating decimals, others yield repeating decimals, and irrational numbers have infinite non-repeating decimal expansions.

History and notation: the decimal system is a base-10 system that originated from Hindu-Arabic numerals. In Europe, decimal fractions were popularized in the 16th century by Simon Stevin. Today, the dot is common as the decimal separator in international contexts, while the comma remains standard in several European conventions.