Question

Classify the following numbers as rational or irrational:

$\left(i\right)\frac{22}{7}\left(ii\right)3.1416\left(iii\right)\pi \left(iv\right)3.\overline{142857}\left(v\right)\mathrm{5.636363...}\left(vi\right)\mathrm{2.040040004...}\left(viii\right)\mathrm{1.535335333....}\left(viii\right)\mathrm{3.121221222...}\left(ix\right)\sqrt{21}\left(x\right)\sqrt[3]{33}$

Answer 1

(i)$\frac{22}{7}$
is rational because it is in the form of$\frac{p}{q}$
, q ≠ 0.

(ii) 3.1416 is rational because it is a terminating decimal.

(iii)$\pi$ is irrational because it is a non-repeating, non –terminating decimal.

(iv)$3.\overline{142857}$is rational because it is a non-terminating, repeating decimal.

(v) 5.636363 = 5.63 is rational because it is a non-terminating, repeating decimal.

(vi) 2.040040004.. is irrational because it is a non-terminating, non-repeating decimal.

(vii) 1.535335333.... is irrational because it is a non-terminating, non-repeating decimal.

(viii) 3.121221222.... is irrational because it is a non-terminating, non-repeating decimal.

(ix) $\sqrt{21}$ is irrational because it is not in the form of p/q

(X)$3\sqrt{3}$ is irrational because it is not in the form of p/q