Meaning & use
rational number
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Meaning
nouncountablemathematics
Any number that can be expressed as one whole number divided by another, where the bottom number is not zero.
Grammar: Takes an article in the singular: 0.75 is a rational number.
Patterns
- a rational number
- the set of rational numbers
The fraction three fifths is a rational number.
Every integer is a rational number because it can be written over one.
A decimal that ends or repeats is a rational number.
Word forms
| plural | rational numbers |
|---|
Common combinations
- set of rational numbers
- The set of rational numbers includes all fractions.
- a positive rational number
- Two thirds is a positive rational number.
- between two rational numbers
- There is always another between two rational numbers.
- express as a rational number
- Try to express 0.125 as a rational number.
- rational number line
- Mark the points on the rational number line.
Synonyms and how they differ
- fraction
- Fraction usually means a ratio written with a numerator and denominator, while rational number is the broader mathematical category that also includes whole numbers and negatives.
- quotient
- A quotient is the result of dividing one number by another, whereas a rational number is a number that can be written as such a quotient of integers.
Opposites
Word family
- rational adjective
- able to be written as a ratio, in mathematics
- rationality noun
- the quality of being rational
- ratio noun
- the relationship between two quantities
- irrational adjective
- not expressible as a ratio of integers
Commonly confused: rational number or irrational number? rational number or real number?
rational number vs irrational number
An irrational number, such as pi or the square root of two, cannot be written as a fraction of integers. A rational number can.
rational number vs real number
Real numbers include both rational and irrational numbers, so rational numbers are only one part.
Practice
Which of these is NOT a rational number?
Choose one answer.
The square root of 2 cannot be written as a fraction of two integers. The other three can be written as 1/2, -7/1 and 3/8.
Make it your own
Write a sentence using “rational number”, then check it and compare it with the examples above.