A decimal is a numeral in the decimal number system.
For example, the decimal expansion of is . The integer part is and the fractional part is
A decimal is terminating if the fractional part has only finitely many decimal digits. It is non-terminating if it has infinitely digits.
For example, is a terminating decimal, whereas , where the pattern 16 repeats indefinitely, is non-terminating.
Non-terminating decimals may be recurring, that is, contain a pattern of digits that repeats indefinitely after a certain number of places.
For example, is a recurring decimal, whereas where the number of 0’s between the 1’s increases indefinitely, is not recurring.
It is common practice to indicate the repeating part of a recurring decimal by using dots or lines as superscripts.
For example, could be written as or
The decimal number system is the base 10, place-value system most commonly used for representing real numbers. In this system positive numbers are expressed as sequences of Arabic numerals 0 to 9, in which each successive digit to the left or right of the decimal point indicates a multiple of successive powers (respectively positive or negative) of 10.
For example, the number represented by the decimal is the sum