Question

Classify the following numbers as rational or irrational:

(i) (ii) (iii) 0.3796

(iv) 7.478478 (v) 1.101001000100001…

Answer 1

(i)

As the decimal expansion of this number is non-terminating non-recurring, therefore, it is an irrational number.

(ii)

It is a rational number as it can be represented in form.

(iii) 0.3796

As the decimal expansion of this number is terminating, therefore, it is a rational number.

(iv) 7.478478 …

As the decimal expansion of this number is non-terminating recurring, therefore, it is a rational number.

(v) 1.10100100010000 …

As the decimal expansion of this number is non-terminating non-repeating, therefore, it is an irrational number.