Question

Classify the following as rational number and irrational number: $\overline{2}$

Answer 1

Definition:

1. Rational number: A rational number is a number that is expressed as $\frac{p}{q}$, where p and q are integers, and $q\ne 0$.

Ex. $2,\frac{1}{4},\frac{11}{7},...$

2. Irrational number: An irrational number is a number that cannot be expressed as $\frac{p}{q}$, where p and q are integers, and $q\ne 0$.

Ex.$\sqrt{2},\sqrt{3},\sqrt{11},...$

3. A non-terminating, non-repeating decimal is an irrational number that continues endlessly, with no group of digits repeating endlessly.

The given number is $\overline{2}$.

Here, $\overline{2}$ is 222… is non-terminating number but it is repeating the same pattern and hence it has a recurring decimal expansion.

Therefore, it is a rational number.