有理数(ゆうりすう)

ゆうりすう
noun
rational number
formalnumberscience
1. rational number
In mathematics, a number that can be expressed as the ratio of two integers (a fraction), where the denominator is not zero. Includes all integers, finite decimals, and repeating decimals. Contrasted with 無理数(むりすう) (irrational numbers) such as π and √2.
有理数(ゆうりすう)と無理数(むりすう)。
Rational and irrational numbers.
分数(ぶんすう)で表(あらわ)せる数(かず)を有理数(ゆうりすう)と呼(よ)ぶ。
Numbers that can be expressed as fractions are called rational numbers.
有理数(ゆうりすう)の集合(しゅうごう)は加減乗除(かげんじょうじょ)について閉(と)じている。
The set of rational numbers is closed under addition, subtraction, multiplication, and division.
中学校(ちゅうがっこう)の数学(すうがく)で、数(かず)を整数(せいすう)、有理数(ゆうりすう)、実数(じっすう)の順(じゅん)に学(まな)ぶ。
In middle school math, students learn numbers in the order of integers, rational numbers, and real numbers.

Formed from 有(ゆう) (having) + 理(り) (reason, ratio) + 数(すう) (number). The 理(り) here refers to a ratio — a rational number is one that "has a ratio," i.e., can be expressed as a ratio of integers.

Usage

  • Standard mathematical term used in middle school, high school, and university education.
  • Often appears alongside 無理数(むりすう) (irrational number) in contrast.
  • The symbol for the set of rational numbers in mathematical notation is ℚ.

Common collocations

  • 有理数(ゆうりすう)の集合(しゅうごう): the set of rational numbers
  • 有理数(ゆうりすう)で表(あらわ)す: to express as a rational number
  • 有理数(ゆうりすう)の加減乗除(かげんじょうじょ): the four operations on rational numbers

Related words

Related Words

Related: 無理数(むりすう) (irrational number)
Related: 整数(せいすう) (integer)
Related: 実数(じっすう) (real number)
Related: 分数(ぶんすう) (fraction)
Related: 小数(しょうすう) (decimal)
general
Added 2026.4.13 1:39 · Revised 2026.9.2 13:02
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