Definitions for repeating decimal
re·peat·ing dec·i·mal

Princeton's WordNetRate this definition:0.0 / 0 votes

1. circulating decimal, recurring decimal, repeating decimalnoun

   a decimal with a sequence of digits that repeats itself indefinitely

WiktionaryRate this definition:0.0 / 0 votes

1. repeating decimalnoun

   A decimal representation of a real number that, at some point, becomes periodic (and repeats the same sequence of digits indefinitely)

WikipediaRate this definition:0.0 / 0 votes

1. Repeating decimal

   A repeating decimal or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely repeated portion is not zero. It can be shown that a number is rational if and only if its decimal representation is repeating or terminating (i.e. all except finitely many digits are zero). For example, the decimal representation of 1/3 becomes periodic just after the decimal point, repeating the single digit "3" forever, i.e. 0.333.... A more complicated example is 3227/555, whose decimal becomes periodic at the second digit following the decimal point and then repeats the sequence "144" forever, i.e. 5.8144144144.... At present, there is no single universally accepted notation or phrasing for repeating decimals. The infinitely repeated digit sequence is called the repetend or reptend. If the repetend is a zero, this decimal representation is called a terminating decimal rather than a repeating decimal, since the zeros can be omitted and the decimal terminates before these zeros. Every terminating decimal representation can be written as a decimal fraction, a fraction whose denominator is a power of 10 (e.g. 1.585 = 1585/1000); it may also be written as a ratio of the form k/2n5m (e.g. 1.585 = 317/2352). However, every number with a terminating decimal representation also trivially has a second, alternative representation as a repeating decimal whose repetend is the digit 9. This is obtained by decreasing the final (rightmost) non-zero digit by one and appending a repetend of 9. Two examples of this are 1.000... = 0.999... and 1.585000... = 1.584999.... (This type of repeating decimal can be obtained by long division if one uses a modified form of the usual division algorithm.) Any number that cannot be expressed as a ratio of two integers is said to be irrational. Their decimal representation neither terminates nor infinitely repeats, but extends forever without repetition (see § Every rational number is either a terminating or repeating decimal). Examples of such irrational numbers are √2 and π.

ChatGPTRate this definition:0.0 / 0 votes

1. repeating decimal

   A repeating decimal, also known as a recurring decimal, is a decimal number that after some point has a finite sequence of digits (known as the repetend or the repeating block) that repeat indefinitely. The simplest example is 0.3333... where the "3" is repeated indefinitely. Other examples include 0.123123123... where "123" is the repeating sequence.

WikidataRate this definition:0.0 / 0 votes

1. Repeating decimal

   In arithmetic, repeating decimal is a way of representing a rational number. Thus, a decimal representation of a number is called a repeating decimal if at some point it becomes periodic, that is, if there is some finite sequence of digits that is repeated indefinitely. For example, the decimal representation of 1/3 = 0.3333333… or 0.3 becomes periodic just after the decimal point, repeating the single-digit sequence "3" infinitely. A somewhat more complicated example is 3227/555 = 5.8144144144…, where the decimal representation becomes periodic at the second digit after the decimal point, repeating the sequence of digits "144" indefinitely. Rational numbers are numbers that can be expressed in the form a/b where a and b are integers and b is non-zero. This form is known as a common fraction. On the one hand, the decimal representation of a rational number is ultimately periodic, as explained below. On the other hand every real number which has an eventually periodic decimal expansion is a rational number. In other words the numbers with eventually repeating decimal expansions are exactly the rational numbers.³²

Matched Categories

1. • Decimal Fraction

How to pronounce repeating decimal?

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   Daniel

   British

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Numerology

1. Chaldean Numerology

   The numerical value of repeating decimal in Chaldean Numerology is: 1

2. Pythagorean Numerology

   The numerical value of repeating decimal in Pythagorean Numerology is: 7

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=repeating decimal
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Repeating_Decimal
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Repeating_Decimal
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=repeating decimal