nonrepeating decimal
LowAcademic, Technical
Definition
Meaning
A decimal number whose digits never form a repeating pattern or sequence.
In mathematics, a decimal expansion that does not become periodic—it does not settle into an infinitely repeating block of digits. This is a characteristic of irrational numbers (like π or √2) and some non-integer rational numbers in specific bases, though in base 10, all rational numbers have either terminating or repeating decimals.
Linguistics
Semantic Notes
Often used synonymously with 'non-terminating, non-repeating decimal' in the context of irrational numbers. The term is definitionally negative, defined by the absence of a repeating pattern.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage. Spelling remains consistent.
Connotations
Purely technical, with no cultural or regional connotative differences.
Frequency
Equally rare in both dialects, confined to mathematics education and discourse.
Vocabulary
Collocations
Grammar
Valency Patterns
The decimal expansion of X is a nonrepeating decimal.X is expressed as a nonrepeating decimal.Vocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Usage
Context Usage
Business
Not used.
Academic
Standard term in mathematics textbooks and courses when discussing number classification and decimal representations.
Everyday
Virtually never used in casual conversation.
Technical
Precise term used in mathematical proofs, number theory, and discussions of numerical computation.
Examples
By Part of Speech
adjective
British English
- The number has a nonrepeating decimal representation.
American English
- It's a nonrepeating decimal expansion.
Examples
By CEFR Level
- Pi is a famous number with a nonrepeating decimal.
- The square root of two is an irrational number, meaning its decimal expansion is nonrepeating and non-terminating.
- While proving the number's transcendence, the mathematician relied on its property of being a nonrepeating decimal in any integer base.
Learning
Memory Aids
Mnemonic
Think of a song that never gets stuck in your head because it has no chorus—its tune is a 'nonrepeating decimal' of notes.
Conceptual Metaphor
A unique, endless path that never loops back on itself.
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Avoid direct calque 'неповторяющаяся десятичная'. The standard term is 'непериодическая десятичная дробь'.
Common Mistakes
- Confusing it with a 'non-terminating decimal', which may still be repeating (like 1/3 = 0.333...).
- Assuming all nonrepeating decimals are irrational; context (e.g., base) is critical.
Practice
Quiz
Which of the following best describes a nonrepeating decimal?
FAQ
Frequently Asked Questions
In the base-10 (decimal) system, yes. If a real number has a nonrepeating decimal expansion, it cannot be expressed as a fraction of two integers and is therefore irrational.
No, not in base 10. By definition, all rational numbers have decimal expansions that either terminate or eventually repeat a block of digits indefinitely.
'Non-terminating' means the decimal goes on forever without ending. 'Nonrepeating' means that in its infinite expansion, no finite block of digits repeats indefinitely. A decimal can be non-terminating but repeating (like 0.666...), or non-terminating and nonrepeating (like π).
Yes, because they cannot be represented exactly in a finite digital system. In computation, we use approximations (like 3.14159 for π) or symbolic representations.