repeating decimal: meaning, definition, pronunciation and examples
C1/C2Formal, Technical, Academic
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
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
Weak
Vocabulary
Antonyms of “repeating decimal”
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
Which of the following is a characteristic of a pure repeating decimal?