Question

State True or False.

(i) Every natural number is a rational number.

(ii) Every integer is a rational number.

(iii) 0 is a whole number, but not a rational number.

Answer 1

(i) A number which can be expressed in the form of $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne 0$, is called a rational number.

Since every natural number can be expressed in the form of a rational number by taking 1 as the denominator $(\frac{1}{1}$, $\frac{2}{1})$, every natural number is a rational number too.

Therefore, statement (i) is true.

(ii) Similarly, every integer can be expressed in the form of a rational number by taking the denominator as 1
$(\frac{-2}{1}$,$\frac{-1}{1}$, $\frac{0}{1}$,$\frac{1}{1}$,$\frac{2}{1})$. So, every integer is a rational number.

Therefore, statement (ii) is true.

(iii) 0, being an integer, is a rational number.

Therefore, statement (iii) is not true.