infinite decimal
C1Academic/Technical
Definition
Meaning
A decimal representation of a number that continues indefinitely without terminating.
Any decimal fraction that has an infinite sequence of digits, which can be either repeating (like a rational number) or non-repeating (like an irrational number such as π or √2).
Linguistics
Semantic Notes
Refers specifically to the representation format of a number, not the abstract concept of infinity itself. The focus is on the form of the numeral, not its value.
Dialectal Variation
British vs American Usage
Differences
No significant lexical difference. 'Decimal' is universally used. The mathematical concepts are identical.
Connotations
Identical technical/mathematical connotation in both varieties.
Frequency
Used exclusively in mathematical/educational contexts with equal frequency.
Vocabulary
Collocations
Grammar
Valency Patterns
The number can be represented [as] an infinite decimal.One third [equals] 0.333..., which is a recurring infinite decimal.√2 is [expressed] as a non-repeating infinite decimal.Vocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “It's an infinite decimal, so we can only work with an approximation.”
Usage
Context Usage
Business
Rarely used, except in highly specialised quantitative finance modelling.
Academic
Central term in mathematics education, number theory, and real analysis.
Everyday
Virtually never used in casual conversation.
Technical
Precise term used in mathematics, computer science (floating-point arithmetic), and engineering.
Examples
By Part of Speech
verb
British English
- The fraction one-seventh will infinite-decimalise to a repeating sequence.
American English
- The fraction one-seventh will infinite-decimalize to a repeating sequence.
adjective
British English
- The number has an infinite decimal representation.
American English
- The number has an infinite decimal representation.
Examples
By CEFR Level
- Some numbers, like one third, go on forever as a decimal.
- When you divide 1 by 3, you get 0.333..., an infinite decimal.
- Pi is an example of an infinite decimal that does not repeat in a predictable pattern.
- The existence of non-repeating infinite decimals like π demonstrates the uncountability of the real numbers.
Learning
Memory Aids
Mnemonic
Think of 'infinite' (without end) + 'decimal' (based on ten). A decimal number that never reaches a final digit.
Conceptual Metaphor
A road that stretches to the horizon and beyond, with mile markers (digits) continuing forever.
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Avoid translating as 'бесконечная десятина' (incorrect). Correct term is 'бесконечная десятичная дробь'.
- Do not confuse with 'иррациональное число' (irrational number). An infinite decimal can represent both rational (repeating) and irrational (non-repeating) numbers.
Common Mistakes
- Using 'infinite' to mean 'very large' instead of 'never-ending' in this context.
- Assuming all infinite decimals are irrational (e.g., 1/3 is rational but is an infinite, repeating decimal).
- Writing '0.333' and calling it an infinite decimal, instead of '0.333...' with ellipsis or a vinculum.
Practice
Quiz
Which of the following is TRUE about an infinite decimal?
FAQ
Frequently Asked Questions
No. Rational numbers like 1/3 (0.333...) are also infinite decimals, but they have repeating patterns.
A recurring (or repeating) decimal has a digit or block of digits that repeats indefinitely (e.g., 0.142857142857...). A non-repeating infinite decimal, like π, has no such repeating pattern.
Typically by writing several digits followed by an ellipsis (...) or, for repeating decimals, by placing a dot or bar over the repeating digit(s), e.g., 0.3̇ or 0.3̄.
No, by definition. We can only write a finite approximation or use symbolic notation (like π or ellipsis) to represent the infinite sequence.