  Question

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) 0 is a rational number.

Solution

(i) True Natural numbers start from 1 to infinity and whole numbers start from 0 to infinity; hence, every natural number is a whole number. (ii) False 0 is a whole number but not a natural number, so every whole number is not a natural number. (iii) True Every integer can be expressed in the $\frac{p}{q}$ form. (iv) False Because whole numbers consist only of numbers of the form $\frac{p}{1}$, where p is a positive number. On the other hand, rational numbers are the numbers whose denominator can be anything except 0. (v) True Every terminating decimal can be easily expressed in the $\frac{p}{q}$ form. (vi) True Every terminating decimal can be easily expressed in the $\frac{p}{q}$ form. (vii) True 0 can be expressed in the form $\frac{p}{q}$, so it is a rational number.MathematicsRS Aggarwal (2017)Standard IX

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