# Definitions for rational numberra·tio·nal num·ber

### Princeton's WordNet(5.00 / 1 vote)Rate this definition:

1. rational number, rational(noun)

an integer or a fraction

### Wiktionary(0.00 / 0 votes)Rate this definition:

1. rational number(Noun)

A real number that can be expressed as the ratio of two integers.

### Wikipedia(3.00 / 2 votes)Rate this definition:

1. Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number. The set of all rational numbers, often referred to as "the rationals", the field of rationals or the field of rational numbers is usually denoted by a boldface Q (or blackboard bold Q {\displaystyle \mathbb {Q} } , Unicode ℚ); it was thus denoted in 1895 by Giuseppe Peano after quoziente, Italian for "quotient". The decimal expansion of a rational number always either terminates after a finite number of digits or begins to repeat the same finite sequence of digits over and over. Moreover, any repeating or terminating decimal represents a rational number. These statements hold true not just for base 10, but also for any other integer base (e.g. binary, hexadecimal). A real number that is not rational is called irrational. Irrational numbers include √2, π, e, and φ. The decimal expansion of an irrational number continues without repeating. Since the set of rational numbers is countable, and the set of real numbers is uncountable, almost all real numbers are irrational.Rational numbers can be formally defined as equivalence classes of pairs of integers (p, q) such that q ≠ 0, for the equivalence relation defined by (p1, q1) ~ (p2, q2) if, and only if p1q2 = p2q1. With this formal definition, the fraction p/q becomes the standard notation for the equivalence class of (p, q). Rational numbers together with addition and multiplication form a field which contains the integers and is contained in any field containing the integers. In other words, the field of rational numbers is a prime field, and a field has characteristic zero if and only if it contains the rational numbers as a subfield. Finite extensions of Q are called algebraic number fields, and the algebraic closure of Q is the field of algebraic numbers.In mathematical analysis, the rational numbers form a dense subset of the real numbers. The real numbers can be constructed from the rational numbers by completion, using Cauchy sequences, Dedekind cuts, or infinite decimals.

### Freebase(3.00 / 1 vote)Rate this definition:

1. Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero. Since q may be equal to 1, every integer is a rational number. The set of all rational numbers is usually denoted by a boldface Q; it was thus named in 1895 by Peano after quoziente, Italian for "quotient". The decimal expansion of a rational number always either terminates after a finite number of digits or begins to repeat the same finite sequence of digits over and over. Moreover, any repeating or terminating decimal represents a rational number. These statements hold true not just for base 10, but also for binary, hexadecimal, or any other integer base. A real number that is not rational is called irrational. Irrational numbers include √2, π, and e. The decimal expansion of an irrational number continues forever without repeating. Since the set of rational numbers is countable, and the set of real numbers is uncountable, almost all real numbers are irrational. The rational numbers can be formally defined as the equivalence classes of the quotient set / ~, where the cartesian product Z × is the set of all ordered pairs where m and n are integers, n is not 0, and "~" is the equivalence relation defined by ~ if, and only if, m1n2 − m2n1 = 0.

### How to pronounce rational number?

1. Alex
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### How to say rational number in sign language?

1.              ### Numerology

1. Chaldean Numerology

The numerical value of rational number in Chaldean Numerology is: 3

2. Pythagorean Numerology

The numerical value of rational number in Pythagorean Numerology is: 1

### Images & Illustrations of rational number

1. ## Translations for rational number

### From our Multilingual Translation Dictionary

• nombre racional
• racionální číslo
• rationale Zahl
• ρητός αριθμός
• racionala nombro
• número racional
• rationaaliluku
• nombre rationnel
• racionális szám
• ռացիոնալ թիվ
• ræð tala
• numero razionale
• 有理数
• 有理數, 유리수
• numerus rationalis
• рационален број
• rationaal getal
• rasjonalt tall
• liczba wymierna
• número racional
• număr rațional
• рациональное число
• racionalni broj, рaционaлни брой
• rationellt tal
• rasyonel sayı

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