Why rational numbers and irrational numbers are in the set of real numbers?

Solution:

A real number is a number that can be represented on a number line. 

Numbers are broadly categorized as real numbers and imaginary numbers.

Unlike rational and irrational numbers, imaginary numbers cannot be represented on a number line.

Hence, rational numbers and irrational numbers are in the set of real numbers.

Why rational numbers and irrational numbers are in the set of real numbers?

Summary:

All those numbers which can be expressed in the form of decimals are real numbers. Since rational and irrational numbers both can be represented as decimals, hence both rational numbers and irrational numbers are in the set of real numbers.