The **key difference between rational and irrational numbers** is, the rational number is expressed in the form of p/q whereas it is not possible for irrational number (though both are real numbers). Learn the definitions, more differences and examples based on them.

## Definition of Rational and Irrational Numbers

**Rational Numbers:** The real numbers which can be represented in the form of the ratio of two integers, say P/Q, where Q is not equal to zero are called rational numbers.

**Irrational Numbers:** The real numbers which cannot be expressed in the form of the ratio of two integers are called irrational numbers.

## What is the Difference Between Rational Numbers and Irrational Numbers?

S.No |
Rational Numbers |
Irrational Numbers |

1 | Numbers that can be expressed as a ratio of two number (p/q form) are termed as a rational number. | Numbers that cannot be expressed as a ratio of two numbers are termed as an irrational number. |

2 | Rational Number includes numbers, which are finite or are recurring in nature. | These consist of numbers, which are non-terminating and non-repeating in nature. |

3 | Rational Numbers includes perfect squares such as 4, 9, 16, 25, and so on | Irrational Numbers includes surds such as √2, √3, √5, √7 and so on. |

4 | Both the numerator and denominator are whole numbers, in which the denominator is not equal to zero. | Irrational numbers cannot be written in fractional form. |

5 | Example: 3/2 = 1.5, 3.6767 | Example: √5, √11 |

Stay tuned with BYJU’S – The Learning App and download the app for Maths-related articles to learn with ease.

## Frequently Asked Questions – FAQs

### What is the main difference between rational and irrational numbers?

### Give an example of rational and irrational numbers?

The examples of irrational numbers are Pi (π) = 3.14159…., Euler’s Number (e) = (2.71828…), and √3, √2.

### How can we identify if a number is rational or irrational?

If a number is non-terminating and non-repeating decimal, then it is irrational, for example, o.31545673…

### Is 2/3 rational or irrational?

We can see, after simplification, 2/3 is a repeating decimal. Hence, it is a rational number.

A non terminating decimal fraction whose decimal part contains digits which are repeated again and again in the same order is called a recurring decimal fraction. All such fractions can be converted to the form p/q so they are rational numbers.