### Topic Page: Decimal

**decimal**

*The Penguin Dictionary of Mathematics*

A number expressed using the decimal number system. Commonly, the term is used for numbers that have fractional parts indicated by a decimal point. A number less than 1 is called a decimal fraction; for example, 0.537 is a way of writing

A mixed decimal is one consisting of an integer and a decimal fraction (e.g. 27.63). The first position to the right of the point (representing tenths) is the first decimal place; the second position is the second decimal place; etc.

A decimal fraction is a series of fractions, i.e. it is a number of tenths plus a number of hundredths plus a number of thousandths, etc. The decimal may have a fixed number of digits: for example, 5/8 is 0.625; such numbers are called finite or terminating decimals. In other decimals the digits may continue indefinitely (they represent an infinite series); decimals of this type are called infinite or nonterminating decimals.

If the number is a rational number it may have an infinitely repeating digit or group of digits; decimals of this type are said to be repeating or recurring decimals.

Thus 1/3 is the decimal 0.333 33 …. This is sometimes written as 0.3 and referred to as ‘nought point three recurring’. Another example of a repeating decimal is 5/7, which is 0.714285 714… with the block of digits 714285 repeated endlessly; this is written as 0.714 285. Such decimals are also called periodic decimals. Irrational numbers, such as π, √2, and e, are decimals that are infinite but do not repeat; such numbers are termed nonrepeating or nonperiodic decimals.

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