What Does Rational Mean?
The word rational has different meanings in different contexts, but generally it refers to something that is based on reason, logic, or facts, rather than emotions, feelings, or opinions. Rational can also describe someone or something that has the ability to think clearly and make sensible decisions. In mathematics, rational can also mean a type of number that can be expressed as a fraction.
Rational
Rational as an Adjective
As an adjective, rational can be used to describe something that is reasonable, sensible, or logical. For example:
A rational plan for economic development
A rational argument / decision
A rational explanation for what happened
Rational can also be used to describe someone who is in full possession of their reason, sanity, or lucidity. For example:
No rational person would behave like that
He was too upset to be rational
She is a calm and rational negotiator
Rational as a Noun
As a noun, rational can refer to a rational number, which is a type of real number that can be written as a fraction, where both the numerator and the denominator are integers and the denominator is not zero. For example:
1/2, 3/4, and -5/6 are rational numbers
0.25, 0.333..., and -1.75 are also rational numbers because they can be written as fractions
√2, Ï, and e are not rational numbers because they cannot be written as fractions
Rational numbers have some properties that distinguish them from other types of numbers, such as:
They are closed under addition, subtraction, multiplication, and division (except division by zero)
They have additive and multiplicative inverses (except zero)
They are ordered and have an absolute value
They have a decimal representation that is either terminating or repeating
Rational vs Irrational
Rational and irrational are often used as opposites in different contexts. For example:
In everyday language, rational means based on reason or logic, while irrational means not based on reason or logic.
In psychology, rational means having sound judgment or good sense, while irrational means having distorted or unrealistic thinking.
In mathematics, rational means a type of number that can be written as a fraction, while irrational means a type of number that cannot be written as a fraction.
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