Decimalformen

Decimalformen, or decimal form, refers to the representation of numbers using the base-10 numeral system with a decimal point that separates the integer part from the fractional part. In decimal form, each digit to the left of the point multiplies a power of ten, while digits to the right denote tenths, hundredths, thousandths, and so on.

Finite decimal forms, or terminating decimals, express rational numbers whose reduced denominator has only factors 2 and 5. If the denominator includes other primes, the decimal form becomes repeating, such as 1/3 = 0.333… or 0.142857142857… for 1/7. Every rational number has a decimal expansion, which may terminate or repeat; irrational numbers do not have a repeating decimal form.

Decimalformen are used in everyday mathematics, measurements, and financial calculations. In computing, decimal values can be represented exactly with fixed-point formats or approximated with floating-point representations, which may introduce rounding errors for certain values (for example, 0.1 is not represented exactly in binary).

Historically, the decimal system derives from Hindu-Arabic numerals. Decimal fractions were popularized in Europe during the early modern period, with figures such as Simon Stevin advocating decimal arithmetic for practical use. Today, decimals are taught as a primary way to express fractions and percentages, and they are commonly converted to and from fractions and scientific notation.