recurring decimal: meaning, definition, pronunciation and examples
C1Academic, Technical, Educational
Quick answer
What does “recurring decimal” mean?
A decimal number in which a digit or group of digits repeats infinitely.
Audio
Pronunciation
Definition
Meaning and Definition
A decimal number in which a digit or group of digits repeats infinitely.
In mathematics, any rational number that, when expressed in decimal form, has a repeating pattern after the decimal point. This contrasts with terminating decimals (which end) and irrational numbers (which have non-repeating, infinite decimal expansions).
Dialectal Variation
British vs American Usage
Differences
British English strongly prefers 'recurring decimal'. American English accepts both 'repeating decimal' and 'recurring decimal', with 'repeating decimal' being more common in standard textbooks.
Connotations
In British academic contexts, 'recurring' is the established, formal term. In American contexts, 'recurring' may sound slightly more technical or British-influenced.
Frequency
High frequency in UK maths education; medium frequency in US maths education, where 'repeating decimal' dominates.
Grammar
How to Use “recurring decimal” in a Sentence
[number] is a recurring decimal[fraction] yields a recurring decimalto recognise [something] as a recurring decimalVocabulary
Collocations
Examples
Examples of “recurring decimal” in a Sentence
verb
British English
- The quotient will begin to recur after the third decimal place.
- Does this fraction recur?
American English
- The calculation caused the digits to recur.
- The pattern is recurring.
adverb
British English
- The digits repeat recurringly.
- The number 0.333... continues recurringly.
American English
- The digits appear recurringly in the output.
- The sequence progressed repeatingly.
adjective
British English
- A recurring decimal expansion is a hallmark of a rational number.
- We studied recurring decimal sequences.
American English
- The repeating decimal notation uses a vinculum.
- She identified the repeating decimal pattern.
Usage
Meaning in Context
Business
Rare. Potentially metaphorical: 'These budget overruns are becoming a recurring decimal in our quarterly reports.'
Academic
Primary context. Used in mathematics, physics, and engineering when discussing numerical representations and precision.
Everyday
Low. Understood by those with secondary maths education, but not common in casual conversation.
Technical
High in mathematical discourse. Essential for describing rational numbers, computational limits, and rounding errors.
Vocabulary
Synonyms of “recurring decimal”
Vocabulary
Antonyms of “recurring decimal”
Watch out
Common Mistakes When Using “recurring decimal”
- Confusing 'recurring' with 'reoccurring' (though related, 'recurring' is the fixed term).
- Using 'recurring decimal' for irrational numbers like π (which are non-repeating).
- Misspelling as 'recuring decimal'.
FAQ
Frequently Asked Questions
In practical mathematical use, they are synonyms. Some purists argue 'recurring' emphasizes the cyclical return, while 'repeating' is more general, but this distinction is rarely upheld.
Yes. By definition, if a number can be expressed as a recurring (or terminating) decimal, it is a rational number (a ratio of two integers).
Common methods are: 1) Placing a dot (or dots) over the repeating digit(s): 0.3̇ for 0.333... 2) Using a vinculum (bar) over the repetend: 0.16‾ for 0.1666... 3) Writing the repeating group in parentheses: 0.16(6).
Yes, there is a standard algebraic method. For example, for 0.363636..., let x = 0.36̅. Then 100x = 36.36̅. Subtracting gives 99x = 36, so x = 36/99 = 4/11.
A decimal number in which a digit or group of digits repeats infinitely.
Recurring decimal is usually academic, technical, educational in register.
Recurring decimal: in British English it is pronounced /rɪˈkɜːrɪŋ ˈdɛsɪm(ə)l/, and in American English it is pronounced /rɪˈkɜːrɪŋ ˈdɛsəməl/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “It's like a recurring decimal (used metaphorically for a persistently repeating event or problem).”
Learning
Memory Aids
Mnemonic
Imagine a RECURring event happening at a DECIMAL point – the same digits keep coming back.
Conceptual Metaphor
NUMBERS ARE PATTERNS (a predictable, endless cycle).
Practice
Quiz
Which of the following best describes the decimal representation of 2/3?