Question

Classify the following numbers into two group and label each group correctly.

(1) $4.\overline{912}$
(2) 0.31045693
(3) $\sqrt{12}$
(4) $\sqrt{49}$
(5) $10.\overline{05}$
(6) 0.1010010001.....

Answer 1

A number in 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 an irrational number.

(1) $4.\overline{912}$
$4.\overline{912}$ has 912 as a recurring term; hence, it is a rational number.

(2) 0.31045693….
In 0.31045693….is non terminating and non repeating decimal number . Hence, it is irrational.

(3) $\sqrt{12}$
Square root of $\sqrt{12}$ is 3.46410161 .
In 3.46410161….is non terminating and non repeating decimal number. Hence, it is irrational.

(4) $\sqrt{49}$
$\sqrt{49}$ can be expressed as 7.
This number is of the form $\frac{p}{q}$, where p = 7 and q = 1 are integers and q ≠ 0.
Hence, $\sqrt{49}$ is a rational number.

(5) $10.\overline{05}$
$10.\overline{05}$ has 05 as a non-terminating and recurring term. Hence, it is a rational number.

(6) 0.1010010001….
In 0.1010010001 …is non terminating and non repeating decimal number . Hence, it is irrational.

Rational	Irrational
$4.\overline{912}$	0.31045693….
$\sqrt{49}$	$\sqrt{12}$
$10.\overline{05}$	0.1010010001….