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# Rational Numbers | Definition, Types and Examples

## Rational Numbers Definition

OR

### What is a rational number?

The numbers of form , where a and b are integers and b is not equal to zero are called rational numbers.

Or we can say that the rational number is the ratio between the two integers a and b.

Rational numbers include all natural numbers, whole numbers, integers, and all fractions with the positive and negative signs. Where b is not zero

### Rational Numbers Examples

• 1\7  is a rational number. Here, a = 1 and b = 7
• -3\8  is a rational number. Here, a = -3 and b = 8
• 2.4 is a rational number because 2.4= 12/5 (12 and 5 are both integers) Here are some others examples which is given below:

Number As a Fraction Rational?
5 5/1 Yes
1.75 7/4 Yes
.002 1/2000 Yes
−0.1 −1/10 Yes
0.111… 1/9 Yes
√5
(square root of 2)
? NO!

Oops! The square root of 5 cannot be formed as a simple fraction! And there are lots of like this type of numbers, and because they are not rational numbers. These numbers are called Irrational.

Another famous irrational number is Pi (π):

pi(π )= 3.14159265358…

## Positive and Negative Rational Numbers

### Positive Rational Numbers

The numerator and denominator of a rational number are either both positive or both negative, the rational number said to be a positive rational number.

#### For Example ### Negative Rational Numbers

The numerator and denominator of a rational number are of opposite signs, one positive and other negative, the rational number is called a negative rational number.

#### For Example ## Frequently Asked Questions on Rational Numbers

### Are natural numbers rational numbers?

Yes, Every natural number is a rational number.

### Is integer a rational number?

Yes, every integer is a rational number.

### Is 0 a rational number?

Yes, 0 is a rational number.

### Is fraction a rational number?

Yes, every fraction a rational number.

### Is 2.4 a rational number?

2.4 is a rational number because 2.4= 12/5 (12 and 5 are both integers).

A fraction is a rational number, but a rational number may or may not be a fraction.