# rational

Pronunciation: say "RASH-uh-nuhl" /ˈɹæʃ(ə)nəl/

## Adjective

1. Mentally sound and balanced, showing good sense and reasonableness.
   - Simple: Thinking in a clear, calm, and sensible way.
   - _Despite the frightening news, she remained rational and made careful decisions._
   - _A rational person weighs the facts before reacting to them._
2. Having the capacity to reason and draw conclusions.
   - Simple: Able to think things through and use reason.
   - _Philosophers long described human beings as rational animals._
   - _A rational creature can weigh options before choosing among them._
3. Sound in its logic, containing nothing self-contradictory or absurd.
   - Simple: Based on clear logic, with no parts that disagree with each other.
   - _The committee accepted his proposal because it was rational and well structured._
   - _A rational explanation should hold together without contradicting itself._
4. In mathematics, describing a number that equals some integer divided by a nonzero integer.
   - Simple: Able to be written as one whole number divided by another.
   - _Every integer is rational, since it can be written over a denominator of one._
   - _The value 0.75 is rational because it equals three-quarters._
6. Of an algebraic expression or function, able to be expressed as the ratio of two polynomials.
   - Simple: Able to be written as one polynomial divided by another.
   - _Engineers often model systems with rational functions like (x²+1)/(x−3)._
   - _The expression is rational because it is a ratio of two polynomials._
7. Of a variety, birationally equivalent to projective space; roughly, geometrically simple almost everywhere.
   - Simple: Of a shape in advanced math, simple nearly everywhere and like a basic flat space.
   - _Every smooth conic over an algebraically closed field is rational._
   - _Proving that a given variety is rational can be extremely difficult._
8. In algebraic geometry, describing a map from one variety to another that need not be defined everywhere but behaves as a morphism on an open part of its domain.
   - Simple: Of a map between shapes in advanced math, working smoothly on an open part of where it is defined.
   - _A rational map need not be defined at every point of its domain._
   - _Projection from a point gives a rational map to the plane._
9. Of a point on a variety over a field, whose coordinates all belong to that field.
   - Simple: Of a point on a shape in advanced math, having all its coordinates in the chosen number system.
   - _Finding rational points on elliptic curves is a central problem in number theory._
   - _A point is rational when its coordinates lie in the base field._
10. Of a formula, expressing the type, structure, relations, and reactions of a compound; graphic.
   - Simple: Of a chemical formula, showing how the parts of a compound are joined, not just which atoms it has.
   - _The chemist wrote out the rational formula to display the compound's bonds._
   - _Older textbooks used rational formulas to show how a compound reacts._
11. Expressing or representing a physical object.
   - Simple: Standing for a real, physical thing rather than just an idea.
   - _In this scheme the expression is rational, standing for a physical object._
   - _Physicists distinguished rational symbols, which name objects, from purely abstract ones._

## Noun

5. A number that can be expressed as the quotient of two integers.
   - Simple: A number you can write as one whole number divided by another.
   - _Between any two rationals there is always another._
   - _Every integer is also a rational._
12. The jeweled breastplate worn by the high priests of ancient Israel.
   - Simple: A jeweled chest piece worn by the high priests of ancient Israel.
   - _The high priest fastened the rational across his chest before entering the sanctuary._
   - _Each stone on the rational stood for one of the twelve tribes._

## Origin

**Meanings 1–11** — From Old French rationel or rational, from Latin rationalis ("belonging to reason, reasonable; having a ratio"), which comes from ratio ("reason; calculation").
**Meaning 12** — From Old French rational, from Medieval Latin rationale ("a pontifical stole or ornament worn over the chasuble"), the neuter of Latin rationalis ("rational"): see the first etymology. It translated Greek λογεῖον (logeîon) or perhaps λόγιον (lógion, "oracle") in the Septuagint version of Exodus 28.

Source: DictionaryAI, https://dictionaryai.com/define/rational (written from Wiktionary data, CC BY-SA 4.0: https://creativecommons.org/licenses/by-sa/4.0/).