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