# 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)

(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.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Champ Quiz | Number Systems43 mins
Genius Quiz | Number Series24 mins
The Curious Case of Irrational Numbers43 mins
Doubts & Quiz - Simplification of Expressions and Laws of Exponents41 mins
Bonus Questions on Rationalization47 mins
Simplification of Expressions and Finding their Values Using Laws of Exponents38 mins
Score more on Number line44 mins
Irrational numbers on Number line32 mins
Terminating & Non - Terminating Decimal Expansion51 mins
Quiz on Irrational Numbers31 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

The number expressed as a vulgar fraction is

RS Aggarwal & V Aggarwal - Mathematics

The simplest form of

RS Aggarwal & V Aggarwal - Mathematics

28. The simplest form of is

RS Aggarwal & V Aggarwal - Mathematics

The simplest form of

RS Aggarwal & V Aggarwal - Mathematics

The simplest form of

RS Aggarwal & V Aggarwal - Mathematics