# How are rational and irrational numbers related?

##### 1 Answer

Rational and irrational numbers are mutually exclusive but jointly or collectively exhaustive set of real numbers.

#### Explanation:

The set of rational numbers and irrational numbers are unique The two most important features are:

**(1)** They are mutually exclusive i.e. a number from one set say Rational numbers

This is because while rational numbers can be written as a ratio of two integers say

In decimal notation, while rational numbers are terminating after decimal sign or have non-terminating but repeating (or recurring decimals), irrational numbers have non-terminating non-repeating (or non-recurring decimals).

**(2)** However, together they form the set of Real numbers

In short, we can say that rational and irrational numbers are mutually exclusive but jointly or collectively exhaustive set of real numbers.