Question

Classify the following numbers as rational or irrational: 

(i) 22 7 

(ii) 3.1416 

(iii) π

(iv) 3. 142857 bar 

(v) 5.636363 

(vi) 2.040040004 

(vii) 1.535335333 

(viii) 3.121221222 

(ix) √21 

(x) 3√3

Answer 1

(i) 22/7 is a rational number because it is of the form of p/q , q ≠ 0. 

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

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

(iv) 3. 142857 bar is a rational number because it is a repeating decimal. 

(v) 5.636363… is a rational number because it is a non-terminating and non-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) √21 = √3 × √7 is an irrational number because √3 and √7 are irrational and prime numbers. 

(x) 3√3  is an irrational number because 3 is a prime number. So, √3 is an irrational number.