Decimális

Decimális, in mathematics, refers to the decimal numeral system (base-10) and to decimal fractions written with a decimal separator. The system uses ten digits, 0 through 9, and a positional notation: the value of a digit depends on its symbol and its position relative to the separator. The part to the left represents whole numbers; the part to the right represents fractional parts.

Decimal separators vary by locale; a dot or a comma may be used. An example is 12.34, meaning twelve and thirty-four hundredths. Decimal fractions in general have denominators that are powers of ten; for example, 0.5 equals 5/10 equals 1/2, and 0.75 equals 75/100 equals 3/4.

Not all decimals terminate. A terminating decimal corresponds to a fraction whose reduced denominator divides a power of ten; otherwise, the decimal representation repeats. For instance, 0.1 terminates, while 0.333... repeats and represents the fraction 1/3.

History and usage: the decimal system relies on place-value notation and the concept of a decimal point or separator. Its modern form emerged from Indian mathematics and was transmitted through the Islamic world to Europe, where Simon Stevin and others popularized decimal fractions in the 16th century. Since then, the decimális system became standard in science, commerce, and education.

Applications: decimals are central in measurement, pricing, and statistical data. They support rounding and precision control, and in computing, decimal arithmetic is implemented via floating-point representations or exact decimal types, depending on the context and required accuracy.