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Infinite decimal expansion

From Encyclopedia of Mathematics
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A number written as a decimal fraction, such that there is no last digit. For example, , or , , etc. If the number is rational, the infinite decimal fraction is recurrent: starting from a certain digit, it consists of an infinitely recurring digit or group of digits called a period. In the above examples these are: 09 for and 0 or 9 for . If the number is irrational, the infinite decimal fraction cannot be recurrent (e.g. ).


Comments

The period length of the decimal expansion of a rational number with not divisible by 2 or 5, is precisely the smallest positive integer such that divides . Thus, the period length divides , the Euler function.

How to Cite This Entry:
Infinite decimal expansion. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Infinite_decimal_expansion&oldid=33414
This article was adapted from an original article by V.I. Bityutskov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article