repeating decimal: meaning, definition, pronunciation and examples

C1/C2
UK/rɪˌpiːtɪŋ ˈdesɪml/US/rɪˌpiːt̬ɪŋ ˈdesəməl/

Formal, Technical, Academic

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Quick answer

What does “repeating decimal” mean?

A decimal number in which a digit or group of digits repeats infinitely after the decimal point.

Audio

Pronunciation

Definition

Meaning and Definition

A decimal number in which a digit or group of digits repeats infinitely after the decimal point.

In mathematics, a rational number whose decimal representation eventually becomes periodic (repeating). It is contrasted with a terminating decimal or an irrational number. The repeating sequence is often indicated with a bar (vinculum) over the repeating digits.

Dialectal Variation

British vs American Usage

Differences

No significant differences in meaning or usage. The concept is identical. Both use the same notation (e.g., a bar over digits or ellipsis).

Connotations

Purely technical and neutral in both varieties.

Frequency

Equally common in academic and educational contexts in both regions.

Grammar

How to Use “repeating decimal” in a Sentence

The fraction yields a repeating decimal.1/3 is a repeating decimal.We represent the repeating decimal with a bar.

Vocabulary

Collocations

strong
infinite repeating decimalnon-terminating repeating decimalpure repeating decimalsimple repeating decimalconverting a fraction to a repeating decimal
medium
identify the repeating decimalnotation for a repeating decimalperiod of the repeating decimalexpress as a repeating decimal
weak
endless repeating decimallong repeating decimalfind the repeating decimal

Examples

Examples of “repeating decimal” in a Sentence

verb

British English

  • The decimal representation will begin to repeat after the third digit.
  • Does it repeat from the start or after a few places?

American English

  • The calculation shows the digits repeat in blocks of six.
  • When you divide it out, the pattern repeats indefinitely.

Usage

Meaning in Context

Business

Virtually never used.

Academic

Core term in mathematics education and number theory.

Everyday

Rare, only in specific educational help contexts.

Technical

Standard, precise term in mathematics, engineering, and computer science when discussing numeric representation and precision.

Vocabulary

Synonyms of “repeating decimal”

Strong

non-terminating repeating decimal

Weak

infinite decimal (if context clarifies repetition)circulating decimal (archaic)

Vocabulary

Antonyms of “repeating decimal”

terminating decimalnon-repeating decimalirrational number (in terms of decimal representation)

Watch out

Common Mistakes When Using “repeating decimal”

  • Writing '0.333' instead of '0.3̅' or '0.333...' to indicate the repetition.
  • Thinking all fractions produce repeating decimals (some produce terminating decimals).
  • Incorrectly placing the repeating bar over non-repeating digits.

FAQ

Frequently Asked Questions

Yes, absolutely. By definition, a repeating decimal represents a rational number (a fraction of two integers).

There is no difference; they are perfect synonyms. 'Recurring decimal' is common in British English, while 'repeating decimal' is used in both American and British English.

The standard notation is to place a horizontal bar (vinculum) over the repeating digit or block of digits. For example, 0.333... is written as 0.3̅.

Yes, the concept applies to all rational numbers. For example, -1/3 = -0.3̅ is a negative repeating decimal.

A decimal number in which a digit or group of digits repeats infinitely after the decimal point.

Repeating decimal is usually formal, technical, academic in register.

Repeating decimal: in British English it is pronounced /rɪˌpiːtɪŋ ˈdesɪml/, and in American English it is pronounced /rɪˌpiːt̬ɪŋ ˈdesəməl/. Tap the audio buttons above to hear it.

Learning

Memory Aids

Mnemonic

Think of a song chorus that REPEATS. A REPEATING DECIMAL has a digit 'chorus' that repeats forever after the decimal point.

Conceptual Metaphor

NUMBERS ARE PATTERNS (The repeating block is a cyclical pattern within the infinite sequence of digits).

Practice

Quiz

Fill in the gap
The fraction 2/7, when expressed as a decimal, results in a .
Multiple Choice

Which of the following is a characteristic of a pure repeating decimal?