What does "irrational" mean?

1. (not logical) not based on reason or clear thinking. 2. (mathematical numbers) describes a number that cannot be written as a simple fraction. 3. (an irrational number) a number that cannot be made by dividing two whole numbers.

irrational

adj. · n.

US //ˌɪˈɹæʃənəɫ// UK //ɪɹˈæʃənəl// ir·ra·tional

1 not logical (adj.)
B2 Upper Intermediate

not based on reason or clear thinking.

lacking logical justification or sound reasoning; often used to describe emotions, fears, or decisions.

Example

She had an irrational fear of spiders, even though she knew they were harmless.

Example

The market's reaction was entirely irrational, driven more by panic and hearsay than by any concrete changes in economic data.
2 mathematical numbers (adj.)
C1 Advanced Technical Math

describes a number that cannot be written as a simple fraction.

relating to a real number that cannot be expressed as a ratio of two integers.

Example

Pi is the most famous example of an irrational number.

Example

The proof that the square root of two is irrational remains a fundamental exercise in introductory number theory.
- rational

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3 an irrational number (n.)
C1 Advanced Technical Math

a number that cannot be made by dividing two whole numbers.

a real number that cannot be expressed as a quotient of two integers.

Example

In this math problem, you need to identify which of these values are irrationals.

Example

The set of real numbers is composed of both rationals and irrationals, though the latter are far more numerous.
- irrational number
- rational

Origin

From Latin irratiōnālis, from ir- + ratiōnālis.