Decimalnotationen

Decimalnotationen (decimal notation) is a system for representing real numbers using base-10 digits and a decimal separator. It is a positional notation in which the value of each digit is determined by its position relative to a decimal separator, with powers of ten for the integer part and negative powers of ten for the fractional part. The digits 0–9 are used, and zero serves as a placeholder to hold place value.

Historically, decimal place-value notation originated in India, spread to the Arab world, and reached Europe in the Middle Ages, where it gradually supplanted other systems. The Hindu–Arabic numerals and the concept of zero enabled compact, scalable representations of numbers and facilitated arithmetic, measurement, and science.

Notational variants: in many European languages the decimal separator is a comma, whereas in English and other contexts a point is used. Thousands separators may be used to group digits (for example, 1,000 or 1 000). In computing, decimals are represented in binary or in decimal floating-point formats; decimal floating-point (for example Decimal128) preserves exact decimal fractions in financial calculations.

Uses and properties: decimal notation enables finite or repeating decimal representations of many numbers and requires rounding for finite representations of irrational or long fractions. It is widely used in education, science, engineering, finance, and everyday measurements, forming the standard basis for most numerical displays and calculations.