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 (irrational numbers) such as π and √2.
有理数と無理数。
Rational and irrational numbers.
分数で表せる数を有理数と呼ぶ。
Numbers that can be expressed as fractions are called rational numbers.
有理数の集合は加減乗除について閉じている。
The set of rational numbers is closed under addition, subtraction, multiplication, and division.
中学校の数学で、数を整数、有理数、実数の順に学ぶ。
In middle school math, students learn numbers in the order of integers, rational numbers, and real numbers.
Formed from 有 (having) + 理 (reason, ratio) + 数 (number). The 理 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 (irrational number) in contrast.
- The symbol for the set of rational numbers in mathematical notation is ℚ.
COMMON COLLOCATIONS:
- 有理数の集合: the set of rational numbers
- 有理数で表す: to express as a rational number
- 有理数の加減乗除: the four operations on rational numbers
RELATED TERMS:
- 無理数: irrational number — cannot be expressed as a fraction (e.g., π, √2)
- 整数: integer — whole numbers, a subset of rational numbers
- 実数: real number — rational and irrational numbers together
- 分数: fraction — the typical form used to write a rational number
- 小数: decimal — finite or repeating decimals are rational