Question:
Define
(i) rational numbers
(ii) irrational numbers
(iii) real numbers.
Solution:
Rational numbers: The numbers of the form $\frac{p}{q}$ where $p, q$ are integers and $q \neq 0$ are called rational numbers.
Example: $\frac{2}{3}$
Irrational numbers: The numbers which when expressed in decimal form are expressible as non-terminating and non-repeating decimals are called irrational numbers.
Example: $\sqrt{2}$
Real numbers: The numbers which are positive or negative, whole numbers or decimal numbers and rational number or irrational number are called real numbers.
Example: $2, \frac{1}{3}, \sqrt{2},-3$ etc.