circulating decimal: meaning, definition, pronunciation and examples
Technical/LowAcademic/Technical
Quick answer
What does “circulating decimal” mean?
A decimal fraction in which a digit or sequence of digits repeats infinitely.
Audio
Pronunciation
Definition
Meaning and Definition
A decimal fraction in which a digit or sequence of digits repeats infinitely.
Also called a repeating decimal. The repeating portion is often indicated by a bar over the digits or dots at the beginning and end.
Dialectal Variation
British vs American Usage
Differences
Both 'circulating decimal' and 'recurring decimal' are standard in British English. In American English, 'repeating decimal' is far more common, while 'circulating decimal' is rarely used.
Connotations
No significant connotative difference; all terms are purely technical.
Frequency
In UK academic contexts, 'recurring decimal' is the dominant term. 'Circulating decimal' is an older, less frequent synonym. In the US, 'circulating decimal' is largely archaic.
Grammar
How to Use “circulating decimal” in a Sentence
X is a circulating decimalThe fraction yields a circulating decimalVocabulary
Collocations
Examples
Examples of “circulating decimal” in a Sentence
verb
British English
- The fraction one-third *circulates* as 0.3 recurring.
- This calculation will *produce* a circulating decimal.
American English
- One divided by seven *yields* a repeating decimal.
- The result *recurs* indefinitely.
adverb
British English
- The digits repeat *cyclically*.
- The number goes on *indefinitely*.
American English
- The three recurs *endlessly*.
- It continues *perpetually*.
adjective
British English
- We studied the *circulating* decimal representation.
- It's a *recurring* decimal phenomenon.
American English
- The *repeating* decimal pattern is clear.
- He explained the *periodic* decimal expansion.
Usage
Meaning in Context
Business
Rarely used. Might appear in very technical financial modelling discussions.
Academic
Primarily used in mathematics education and number theory.
Everyday
Virtually never used. Most people say 'repeating decimal' or describe it (e.g., 'point three repeating').
Technical
The standard, precise term in mathematical discourse, though 'repeating decimal' is equally technical.
Vocabulary
Synonyms of “circulating decimal”
Strong
Weak
Vocabulary
Antonyms of “circulating decimal”
Watch out
Common Mistakes When Using “circulating decimal”
- Misspelling as 'circulat*ing* decimal'. Confusing it with a 'non-terminating, non-repeating' (irrational) decimal.
FAQ
Frequently Asked Questions
Yes, they are exact synonyms. 'Repeating decimal' (or 'recurring decimal' in UK English) is the more common modern term.
Typically by placing a horizontal bar (vinculum) over the repeating digit(s), e.g., 0.3̅, or by using dots above the first and last repeating digits, e.g., 0.1̇6̇.
No. Non-terminating decimals include both repeating (rational) decimals and non-repeating (irrational) decimals like π or √2.
The term 'circulating decimal' is now quite rare. It might be found in older mathematical texts. In modern academic or everyday use, 'repeating decimal' is strongly preferred.
A decimal fraction in which a digit or sequence of digits repeats infinitely.
Circulating decimal is usually academic/technical in register.
Circulating decimal: in British English it is pronounced /ˈsɜː.kjə.leɪ.tɪŋ ˈdes.ɪ.məl/, and in American English it is pronounced /ˈsɝː.kjə.leɪ.t̬ɪŋ ˈdes.ə.məl/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “It's like a circulating decimal—it just goes on and on.”
Learning
Memory Aids
Mnemonic
Imagine digits running in a circle on a track—they circulate forever.
Conceptual Metaphor
NUMBERS ARE MOTION (circulating), PATTERNS ARE CYCLES.
Practice
Quiz
Which of the following is a synonymous term for 'circulating decimal'?