Question

Classify the following number as rational or irrational:
(i) $$ \dfrac {22}{7} $$

(ii) $$ 3.1416 $$

(iii) $$ \pi $$

(iv)$$ 3.\overline{142857}$$

(v) $$5.636363....$$

(vi)$$2.040040004...$$

(vii) $$1.535335333....$$

(viii) $$3.121221222....$$

(ix) $$ \sqrt {21} $$

(x) $$ \sqrt [3]{3} $$

Answer 1

(i) $$ \dfrac {22}{7} $$ is rational number. since the no. is in its simplest form.

(ii) $$ 3.1416 $$ is rational number.it is terminating and non -repeating decimal.

(iii) $$ \pi $$ irrational number it is a non -terminating and non -repeating decimal

(iv)$$ 3.\overline{142857} $$ A rational number. Non-terminating repeating decimal.

(v) $$5.636363....$$
A rational number. A non -terminating repeating decimal.

(vi)$$2.040040004$$...
An irrational number . A non -terminating and non -repeating decimal.

(vii) $$1.535335333....$$
An irrational number . A non -terminating and non -repeating decimal.

(viii) $$3.121221222....$$
An irrational number . A non -terminating and non -repeating decimal.

(ix) $$ \sqrt {21} $$
An irrational number. $$ 21 = 3 \times 7 $$ is an irrational number and 3 and 7 are are prime and irrational numbers.

(x) $$ \sqrt [3]{3} $$
An irrational number . 3 is a prime number so 3 is an irrational number.