All numbers including both rational and irrational numbers are called Real Numbers.
Real Numbers and their Decimal Expansions
1. Rational Numbers
If the rational number is in the form of then by dividing a by b we can get two situations.
a. If the remainder becomes zero
While dividing if we get zero as the remainder after some steps then the decimal expansion of such number is called terminating.
b. If the remainder does not become zero
While dividing if the decimal expansion continues and not becomes zero then it is called non-terminating or repeating expansion.
It can be written as
Hence, the decimal expansion of rational numbers could be terminating or non-terminating recurring and vice-versa.
2. Irrational Numbers
If we do the decimal expansion of an irrational number then it would be non –terminating non-recurring and vice-versa. i. e. the remainder does not become zero and also not repeated.