# Rational vs. Irrational: What's the Difference?

Edited by Aimie Carlson || By Janet White || Published on November 16, 2023
Rational refers to logical thinking or reasonability, while irrational denotes the absence of logic or reason.

## Key Differences

The term "rational" is rooted in the idea of reason and logic. When something is rational, it adheres to the principles of sound judgment and thinking. It suggests clarity, coherence, and a basis in factual understanding, especially in contexts where decision-making or evaluation is essential.
On the other hand, "irrational" stands as the antithesis to rationality. An irrational action, thought, or decision lacks logic or clear reasoning. It's driven more by emotions, misconceptions, or impulsive tendencies than by a well-constructed rationale. This doesn't necessarily mean it's wrong or detrimental, but it's not grounded in sound logic.
When discussing numbers, the terms take on more specific meanings. A rational number is any number that can be expressed as a fraction of two integers. For instance, the number 1/2 or 0.5 is rational. Conversely, an irrational number cannot be precisely represented as a simple fraction. Numbers like the square root of 2 or π (pi) are examples of irrational numbers.
In human behavior, being rational is often equated with being level-headed and making decisions based on objective data. However, irrational behavior, often stemming from emotions or misconceptions, is also an intrinsic part of human nature. Both rational and irrational elements coexist, influencing decisions and actions.

## Comparison Chart

### Definition

Based on logic and reasoning
Not based on or against logic and reasoning

### Nature

Logical, systematic
Emotional, impulsive

### In Mathematics

Numbers representable as fractions
Numbers not representable as simple fractions

### In Decision Making

Decisions based on facts and analysis
Decisions based on emotion or impulse

### Behavior

Analytical, reasonable
Spontaneous, unpredictable

## Rational and Irrational Definitions

#### Rational

Based on clear thought and reason.
Her rational approach to the problem led to a quick solution.

#### Irrational

Not logical or reasonable.
Her fear of the color blue is completely irrational.

#### Rational

Understandable and reasonable.
His fear of heights is perfectly rational.

#### Irrational

Beyond human understanding.
The vastness of the universe can seem irrational to many.

#### Rational

Sound in judgment.
It's rational to save money for future needs.

#### Irrational

Not endowed with reason.

#### Rational

Representable as a quotient of two integers.
The number 3/4 is a rational number.

#### Irrational

Affected by loss of usual or normal mental clarity; incoherent, as from shock.

#### Rational

Having or exercising the ability to reason.

#### Irrational

Marked by a lack of accord with reason or sound judgment
An irrational dislike.

#### Rational

Consistent with or based on reason or good judgment; logical or sensible
Rational decisions.

#### Irrational

Being a syllable in Greek and Latin prosody whose length does not fit the metric pattern.

#### Rational

Of sound mind; sane
Wondered if the eccentric neighbor was not completely rational.

#### Irrational

Being a metric foot containing such a syllable.

#### Rational

(Mathematics) Capable of being expressed as a quotient of integers.

#### Irrational

(Mathematics) Of or relating to an irrational number.

#### Rational

A rational number.

#### Irrational

An irrational number.

#### Rational

Capable of reasoning.
Man is a rational creature.

#### Irrational

Not rational; unfounded or nonsensical.
An irrational decision

#### Rational

Logically sound; not self-contradictory or otherwise absurd.
His statements were quite rational.

#### Irrational

Of a real number, that cannot be written as the ratio of two integers.
The number π is irrational.

#### Rational

(of a person or personal characteristics) Healthy or balanced intellectually; exhibiting reasonableness.
Rational conduct

#### Irrational

A real number that can not be expressed as the quotient of two integers, an irrational number.

#### Rational

Of a number, capable of being expressed as the ratio of two integers.
¾ is a rational number, but √2 is an irrational number.

#### Irrational

Not rational; void of reason or understanding; as, brutes are irrational animals.

#### Rational

Of an algebraic expression, capable of being expressed as the ratio of two polynomials.

#### Irrational

Not according to reason; having no rational basis; clearly contrary to reason; easily disproved by reasoning; absurd; - of assertions and beliefs.
It seemed utterly irrational any longer to maintain it.

#### Rational

(chemistry) Expressing the type, structure, relations, and reactions of a compound; graphic; said of formulae.

#### Irrational

Not capable of being exactly expressed by an integral number, nor by a ratio of integral numbers; surd; - said especially of roots. See Surd.

#### Rational

(physics) Expressing a physical object.
A rational table is physical, a written table is neither.

#### Irrational

Not consistent with or using reason;
Irrational fears
Irrational animals

#### Rational

(mathematics) A rational number: a number that can be expressed as the quotient of two integers.
The quotient of two rationals is again a rational.

#### Irrational

Real but not expressible as the quotient of two integers;
Irrational numbers

#### Rational

(historical) The breastplate worn by Israelite high priests.

#### Irrational

Not expressible as an exact fraction of two integers.
The square root of 2 is an irrational number.

#### Rational

Relating to the reason; not physical; mental.
Moral philosophy was his chiefest end; for the rational, the natural, and mathematics . . . were but simple pastimes in comparison of the other.

#### Irrational

Not governed by clear thought.
His decision to give away all his possessions was seen as irrational.

#### Rational

Having reason, or the faculty of reasoning; endowed with reason or understanding; reasoning.
It is our glory and happiness to have a rational nature.

#### Irrational

Acting without sound judgment.
In his anger, he made an irrational choice.

#### Rational

Agreeable to reason; not absurd, preposterous, extravagant, foolish, fanciful, or the like; wise; judicious; as, rational conduct; a rational man.

#### Rational

Expressing the type, structure, relations, and reactions of a compound; graphic; - said of formulæ. See under Formula.
What higher in her society thou find'stAttractive, human, rational, love still.
A law may be reasonable in itself, although a man does not allow it, or does not know the reason of the lawgivers.

#### Rational

A rational being.

#### Rational

Consistent with or based on or using reason;
Rational behavior
A process of rational inference
Rational thought

#### Rational

Of or associated with or requiring the use of the mind;
Intellectual problems
The triumph of the rational over the animal side of man

#### Rational

Capable of being expressed as a quotient of integers;
Rational numbers

#### Rational

Having its source in or being guided by the intellect (distinguished from experience or emotion);
A rational analysis

#### Rational

Having the capacity to reason.
Humans are generally considered rational beings.

## FAQs

#### Are all whole numbers rational?

Yes, all whole numbers can be expressed as fractions (e.g., 5 is 5/1), making them rational.

#### Does rational always mean correct?

No, something can be rationally derived but still be incorrect due to flawed premises.

#### Can someone be rational and emotional simultaneously?

Yes, emotions and rationality can coexist; recognizing emotions can be part of rational decision-making.

#### Is zero a rational number?

Yes, zero can be expressed as 0/1, making it a rational number.

#### Why are some numbers, like π (pi), considered irrational?

Numbers like π cannot be precisely represented as a simple fraction, making them irrational.

#### Are animals capable of rational thought?

While animals can exhibit complex behaviors, whether they possess human-like rationality is still debated.

#### Can irrational decisions lead to positive outcomes?

Yes, outcomes from irrational decisions can sometimes be beneficial, though they lack logical reasoning.

#### Is every fraction a rational number?

Yes, every fraction with an integer numerator and a non-zero integer denominator is a rational number.

#### Can a belief be both rational and irrational?

Depending on the context and individual perspective, a belief can be viewed as either rational or irrational.

#### Can rationality be learned or improved upon?

Yes, with education and practice, one can enhance their rational thinking skills.

#### Can someone be mostly rational or mostly irrational?

Yes, while everyone has moments of both, an individual can predominantly exhibit one over the other.

#### Are humans always rational?

No, humans can be influenced by emotions, biases, and other factors leading to irrational behavior.

#### Can an irrational number be approximated as a fraction?

Yes, irrational numbers can be approximated using fractions, but not exactly represented.

#### Is the number e (Euler's number) rational or irrational?

The number e is irrational.

#### Is it better to be rational or irrational?

Neither is inherently better. Rationality is favored in logical decision-making, while irrationality can be valuable in creative processes. Balance is key.

#### Do cultural differences influence what's considered rational?

Yes, cultural norms and values can shape perceptions of rationality.

#### Is it irrational to act on gut feelings?

Not necessarily; intuition can be based on subconscious reasoning, but it's not always logically explainable.

#### Why is understanding the difference between rational and irrational important?

It aids in effective decision-making, understanding human behavior, and learning mathematical concepts.

#### What's the connection between rational thought and critical thinking?

Rational thought is a component of critical thinking, which also involves analyzing, evaluating, and synthesizing information.

#### Can art be rational or irrational?

Art can embody both rational elements (like structured compositions) and irrational elements (like abstract emotions).