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2

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

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)

∵ we can not simplify or in integer form,

Hence, it is an irrational number.

(vi)

∵ we can not simplify or in integer form,

Hence, it is an irrational number.

(vii)

=

∵ we can not simplify or √2 in integer form,

Hence, it is an irrational number.

(viii)

∵ we know that all repeating decimals are rational,

Hence, it is a rational number.

(ix) 1.232332333…

∵ we know that non-terminating decimals never repeats and cannot be represented as a quotient of two integers,

Hence, it is an irrational number.

(x) 3.040040004…

∵ we know that non terminating decimals never repeats and can not be represented as a quotient of two integers,

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 terminating 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.