dezimaler

Dezimaler is the plural form of dezimal, used in several languages to refer to decimal numbers or decimal fractions. In mathematics, dezimaler denote numbers written in the base-10 numeral system using a decimal point to separate an integer part from a fractional part. A decimal number has digits to the left of the decimal point representing integer place values (10^0, 10^1, 10^2, etc.) and digits to the right representing fractional place values (10^-1, 10^-2, etc.).

Notation and variants: The decimal point is the standard separator in many countries, while some regions use a comma. Decimal expansions can be finite (e.g., 12.5) or infinite. A rational number has a terminating decimal expansion if, after reduction, its denominator has only the prime factors 2 and 5. Otherwise its decimal expansion is infinite and non-terminating, often repeating (e.g., 1/3 = 0.333…).

Operations and uses: Decimals are used for precise measurement, financial calculations, and scientific data. Arithmetic with decimals aligns the decimal points and carries across fractional digits. Rounding and significant figures are common to express decimals with an appropriate precision. Decimals also arise by dividing integers and are converted to fractions by placing the decimal point according to the division result.

History and context: The base-10 decimal system has ancient roots and became widespread due to its place-value structure and ease of arithmetic. Dezimaler are widely used worldwide, bridging everyday measurements, computations, and numeric notation.

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