### What are rational numbers?

Numbers of the form^{p}/

_{q}, where p and q are integers and q≠0 are called

__rational numbers__. In other words, rational numbers are the set of all ratios made up of real numbers, which do not have zero as denominator. Rational numbers are a type of real numbers. The set of rational numbers is denoted by “Q”. Rational numbers include natural numbers, whole numbers, integers and fractions.

Between any two numbers there can be infinite rational numbers.

**Rational numbers are subdivided into:**

•

**Integers**: Rational numbers of the form

^{p}/

_{q}where q= ±1 are called integers.

•

**Fractions**: Rational numbers of the form

^{p}/

_{q}where q ≠ 0 and p<q are called fractions. They can also be expressed as decimals.

Terminating decimals and recurring decimals are rational numbers.

**A recurring decimal**is one which has one or more digits after the decimal point and they repeat endlessly in a specific pattern. Any recurring decimal can be expressed as a fraction. Hence it is a rational number. The pattern of rational numbers which is repeated is denoted by a line above the pattern called “bar” or “vinculum”. For example

^{1}/

_{3}= 0.3333…,

^{-2}/

_{3}= -0.6666…,

^{1}/

_{9}= 0.1111… are fractions which can be converted to recurring decimals.

**A terminating decimal**is one in which has limited number of numbers after the decimal place. Any terminating decimal can be expressed as a fraction. Hence it is a rational number. For example

^{5}/

_{8}= 0.625,

^{3}/

_{2}= 1.5,

^{3}/

_{4}= 0.75 are fractions which can be converted to terminating decimals.

*List of Some Rational Numbers :-*Rational numbers |

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What Are Perfect Numbers?

List of Prime Numbers

Irrational Numbers

Definition of Real Number

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