whole number
B1Formal to Neutral (primarily academic/educational)
Definition
Meaning
An integer (e.g., 0, 1, 2, 3, ...) including zero, but not fractions or decimals.
A number without a fractional or decimal component. In everyday contexts, sometimes used to mean a natural number (1, 2, 3...), but in precise technical and educational contexts, its definition explicitly includes zero and negative integers.
Linguistics
Semantic Notes
Its meaning is highly dependent on context. In primary mathematics, it often means positive integers only. In secondary/university contexts, it's synonymous with 'integer' (including zero and negatives). The ambiguity can cause confusion if not clarified.
Dialectal Variation
British vs American Usage
Differences
Slight. UK curricula may more frequently use the term in early education. The term 'integer' is preferred in more advanced contexts universally. No difference in formal definition.
Connotations
Neutral, academic. May evoke primary school maths lessons.
Frequency
Moderate and stable in educational materials in both regions. Rare in casual conversation outside of teaching/learning contexts.
Vocabulary
Collocations
Grammar
Valency Patterns
[be] a whole number[express/represent/write] [something] as a whole number[round up/down] to a whole numberVocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “[not] a whole number (used to emphasize something is fractional or incomplete, e.g., 'My share of the bill wasn't a whole number, so I paid the extra pence.')”
Usage
Context Usage
Business
Used in accounting or reporting when figures are rounded, e.g., 'Report profits in whole numbers of thousands.'
Academic
Core term in mathematics education and foundational number theory.
Everyday
Used when discussing rounding or simple counting, e.g., 'Give me a whole number between 1 and 10.'
Technical
Precisely defined as an element of the set of integers ℤ. Used in programming, data types (e.g., INT).
Examples
By Part of Speech
adjective
British English
- We need a whole-number solution.
- The result must be whole-number.
American English
- We need a whole-number answer.
- The data is in whole-number format.
Examples
By CEFR Level
- Five is a whole number.
- You can't have half a person; you need a whole number.
- Please round your answer to the nearest whole number.
- The recipe requires a whole number of eggs.
- The function is only defined for whole number inputs.
- Negative seven is also considered a whole number in this course.
- The algorithm discretises the continuous variable into a set of whole number intervals.
- The theorem holds for all whole number exponents, including zero and negative integers.
Learning
Memory Aids
Mnemonic
Think of a WHOLE pie, not a slice. A 'whole number' is complete, not broken into fractions.
Conceptual Metaphor
NUMBERS ARE OBJECTS (whole objects vs. broken pieces). COMPLETENESS IS WHOLENESS.
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Avoid confusing with 'целое число' which is a direct and correct translation for 'integer'. The trap is the ambiguous use in basic English materials where it might exclude negative numbers, while 'целое число' in Russian always includes them.
Common Mistakes
- Using 'whole number' to mean 'natural number' (only positive) in advanced contexts where 'integer' is required.
- Confusing it with 'real number' or 'rational number'.
- Thinking zero is not a whole number (it is in standard mathematical definitions).
Practice
Quiz
Which of the following is NOT necessarily true about a whole number in a standard secondary-level mathematics definition?
FAQ
Frequently Asked Questions
Yes, in modern standard mathematical definitions, the set of whole numbers includes zero, positive integers (1, 2, 3...), and often negative integers (-1, -2, -3...), making it synonymous with 'integers'.
Traditionally, 'natural numbers' refer to the counting numbers 1, 2, 3... (sometimes including zero). 'Whole numbers' formally include zero and often all integers. In casual use, they are sometimes confused, but in precise terms, 'whole number' has a broader scope.
No. By definition, a whole number has no fractional or decimal component. Numbers like 5.0 are conceptually equal to the whole number 5, but the notation '.0' is a decimal representation of an integer value.
Rarely. In university-level mathematics and professional STEM fields, the precise term 'integer' is universally preferred to avoid the ambiguity associated with 'whole number' from earlier education.