Question

Classify the following numbers as rational or irrational:

(i) $\frac{22}{7}$
(ii) 3.1416
(iii) π
(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) $\frac{22}{7}$ is a rational number because it is of the form of $\frac{p}{q},q$≠ 0.

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

(iii) $\mathrm{\pi }$ is an irrational number because it is a non-repeating and non-terminating decimal.

(iv) 3.142857 is a rational number because it is a repeating decimal.

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

(vi) 2.040040004... is an irrational number because it is a non-terminating and non-repeating decimal.

(vii) 1.535335333... is an irrational number because it is a non-terminating and non-repeating decimal.

(viii) 3.121221222... is an irrational number because it is a non-terminating and non-repeating decimal.

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

(x) $\sqrt[3]{3}$ is an irrational number because 3 is a prime number. So, $\sqrt{3}$ is an irrational number.