decimalrepresentation

Decimal representation is the notation of numbers in base ten using digits 0 through 9 and a decimal point. Each real number is written as an integer part and a fractional part, with place values corresponding to powers of ten: units, tens, hundreds to the left; tenths, hundredths, thousandths to the right. The representation can be finite for some numbers or infinite for others.

A real number has a terminating decimal expansion if, after reducing the fraction, the denominator has only the prime factors 2 and 5. For example, 3/8 equals 0.375 and terminates. If the reduced denominator contains other primes, the decimal expansion is infinite and repeats periodically; for instance, 1/3 equals 0.333… and 1/7 equals 0.142857142857… repeating.

Irrational numbers, such as pi, e, or sqrt(2), have non-terminating, non-repeating decimal expansions, meaning their digits do not settle into a repeating block and cannot be expressed exactly with a finite or repeating sequence of digits.

Decimal representations can be rounded or truncated to a desired precision. In some locales, the decimal separator is a comma rather than a point. There is a standard but non-unique aspect: numbers like 0.4999… and 0.5 are equal, as are 1.999… and 2. Decimal representations enable measurement, computation, and communication of real numbers across science and daily life.