NCERT Solutions for Class 9 Maths Chapter 1 Number Systems

Ans : Zero is a rational number as it can be represented as \(\frac{0}{1} \text { or } \frac{0}{2} \text { or } \frac{0}{3}\) etc. 

Ans : There are infinite rational numbers in between 3 and 4.  
 \(\begin{array}{l}{3 \text { and } 4 \text { can be represented as } \frac{24}{8} \text { and } \frac{32}{8}} \\ {\text { Therefore, rational numbers between } 3 \text { and } 4 \text { are }} \\ {\frac{25}{8}, \frac{26}{8}, \frac{27}{8}, \frac{28}{8}, \frac{29}{8}, \frac{30}{8}}\end{array}\) 

Ans : \(\begin{array}{l}{\text { There are infinite rational numbers between } \frac{3}{5}} & {\text { and } \frac{4}{5}} \\ {\frac{3}{5}=\frac{3 \times 6}{5 \times 6}=\frac{18}{30}} \\ {\frac{4}{5}=\frac{4 \times 6}{5 \times 6}=\frac{24}{30}}\end{array}\)   
Therefore, rational numbers between \(\frac{3}{5} \text { and } \frac{4}{5}\).
\(\frac{19}{30}, \frac{20}{30}, \frac{21}{30}, \frac{22}{30}, \frac{23}{30}\) 

Ans : (i) True; since the collection of whole numbers contains all natural numbers.  
(ii) False; as integers may be negative but whole numbers are positive.
For example: —3 is an integer but not a whole number.  
(iii) False; as rational numbers may be fractional but whole numbers may not be.
For Example :\(\frac{1}{5}\) is rational number but not a whole number. 

Ans : (i) True; since the collection of real numbers is made up of rational and irrational numbers.  
(ii) False; as negative numbers cannot be expressed as the square root of any other number.  
(iii) False; as real numbers include both rational and irrational numbers. Therefore, every real number cannot be an irrational number.