Question

Classify the following numbers as rational or irrational numbers.

(1) $2.\overline{18}$
(2) $\sqrt{19}$
(3) $\sqrt{1.96}$
(4) 4.81231659

Answer 1

A number of the non-terminating, recurring decimal form is a rational number and a number whose decimal form is non- terminating but is not recurring is called irrational number.

(1) $2.\overline{18}$
$2.\overline{18}$ has 18 as a recurring term. Also, it is non-terminating.Hence, it is a rational number.

(2) $\sqrt{19}$
$\sqrt{19}$ = 4.358…… The decimal number is non-terminating and non-repeating. Hence, this number is irrational.

(3) $\sqrt{1.96}$
$\sqrt{1.96}$ = 1.4
1.4 can be written as $\frac{14}{10}=\frac{7}{5}$
This number is of the form $\frac{p}{q}$, where p = 7 and q = 5 are integers and q ≠ 0
So, $\frac{7}{5}$ is a rational number, i.e. $\sqrt{1.96}$ can be written as a rational number.

(4) 4.81231659….
In 4.81231659….the decimal number is non-terminating and non-repeating. Hence, this number is irrational.