**What is Rational Number**

A **rational numbers** are numbers that can be expressed as a ratio of two integers.

All integers belong to the rational numbers. A rational number a/b is said to have numerator a and denominator b. Numbers that are not rational are called irrational numbers.

*a*b , b≠0

Where a and b are both integers.

**Conditions for Rational Number**

1. The limited number of digits after the decimal point.

**For example**, 5.4321.

2. The infinitely repeating number after the decimal point.

**For example**, 2.333333…

3. The infinitely repeating pattern of numbers after the decimal point.

**For example**, 3.151515…

**Example:**

• 3/7: Here 3 is an integer, 7 is an integer so yes it is a rational number.

• 0/0: Here there is 0 in the denominator. So it is not a rational number.

• -5: Here -9 can be written −5/1. So it is a rational number.

• 0: 0 is a rational number.

• 0.75 Here (3/4) can be written. So it is a rational number.

• 2.12 Here (212/100) can be written. So it is a rational number.

**Positive Rational Numbers**: If both the numerator and denominator have the same signs is called Positive Rational Numbers.

**For example:** *+ 2*+ 5 , *– 2*– 5

**Negative Rational Numbers**: If both the numerator and denominator have different signs is called Negative Rational Numbers.

**For example:** *+ 2*– 5 , *– 2*+ 5

**Properties of Rational Number**

1. A rational number remains unchanged when a non zero integer is multiplied to both numerator and denominator.

**For example:** *2 x 5*3 x 5 = *2*3

1. A rational number remains unchanged when a non zero integer is divided to both numerator and denominator.

**For example:** *2 ÷ 5*3 ÷ 5 = *2*3

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I hope you have learned it properly.