Q. 44.4( 18 Votes )

Write, whether the given statement is true or false. Give reasons.

(i) Every natural number is a whole number.

(ii) Every whole number is a natural number.

(iii) Every integer is a rational number.

(iv) Every rational number is a whole number.

(v) Every terminating decimal is a rational number.

(vi) Every repeating decimal is a rational number.

(vii) 0 is a rational number.

Answer :

(i) True: every natural number is the whole number because natural number starts with 1 and whole number start with 0. So, every natural number will automatically fall in the category of whole number.


(ii) False: every whole number can’t be natural number as natural number starts from 1 and whole number starts with 0.


(iii) True: Integers includes all whole numbers and their negative counterparts. Rational numbers can be expressed in the form of fractions where denominator is not equals to the zero but both, numerator and denominator are integers.


(iv) False: Rational number is the number which can be expressed in the form of fraction where denominator is not equals to zero. But whole numbers are natural numbers including zero and they can’t be written in fractional form.


(v) True: Rational number is the number which can be expressed in the form of fraction where denominator is not equals to zero and terminating decimal can also be written in fraction form.


(vi) True: Yes, every repeating decimal is also the rational number because it also written in the form of fraction.


(vii) True: yes, 0 is also the rational number because it can be written in the form of fraction.


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