Q. 23.8( 12 Votes )

Classify the following numbers as rational or irrational. Give reasons to support your answer.

(i) (ii) (iii)

(iv) (v) (vi)

(vii) (viii) (ix) 1.232332333…

(x) 3.040040004… (xi) 3.2576

(xii) 2.3565656… (xiii)(xiv)

Answer :

(i)


=


∵ we can express 2 as which is the quotient of the integer 2 and 1


Hence, it is a rational number.


(ii)


=


∵ we can express 14 as which is the quotient of the integer 14 and 1


Hence, it is a rational number.


(iii)


=


∵we can not simplify  in the form 


Hence, it is an irrational number.


(iv)


We know that 43 is a prime number so we can not get prime factors of it and neither we can write in fractional form.


Hence, it is an irrational number.


(v)


∵  is irrational number and addition of an irrational number to any real number always gives irrational number.


Hence, it is an irrational number.


(vi)


 is irrational number and addition of an irrational number to any real number always gives irrational number.


Hence, it is an irrational number.


(vii)


=


∵ As,  and √2 are irrational numbers and multiplication of an irrational  number to a non zero rational number gives irrational number.


Hence, it is an irrational number.


(viii)


∵ we know that all repeating decimals are rational,


Hence, it is a rational number.


(ix) 1.232332333…


∵ The decimal expansion here is non terminating and non repeating,


Hence, it is an irrational number.


(x) 3.040040004…


∵ The decimal expansion here is non terminating and non repeating,


Hence, it is an irrational number.


(xi) 3.2576


∵ It is a terminating decimal fraction and can be expressed in form


Hence it is a rational number.


(xii) 2.3565656…


∵ it is a non terminating but repeating decimal form that can be written as 2.35.


Hence, it is a rational number.


(xiii)


∵ We know that π is a non terminating Decimal fraction,


Hence it is an irrational number.


(xiv)


∵ it is an fractional form,


Hence it is rational.

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