NCERT Class 9 Maths Solutions Chapter - 1 Number Systems, Ex 1.1

Ex - 1.1

Question 1.  Is zero a rational number? Can you write it in the form , where p and q are integers and q  0?

Solution

Yes zero is a rational number as it can be represented in the   form,  where p and q are integers and q  0 as  etc.

Concept Insight: Key idea to answer this question is "every integer is a rational number and zero is a non negative integer".  Also 0 can be expressed in  form in various ways as 0 divided by any number is 0. simplest is   .

Question 2.  Find six rational numbers between 3 and 4.

Solution

There are infinite rational numbers in between 3 and 4.
3 and 4 can be represented as respectively.

Now rational numbers between 3 and 4 are  
    

Concept Insight:  Since there are infinite number of rational numbers between any two numbers so the answer is not unique here.  The trick is to convert the number to equivalent  form by multiplying and dividing by the number atleast 1 more than the rational numbers to be inserted.

Question 3.  Find five rational numbers between  .

Solution

There are infinite rational numbers between 

         

        

Now rational numbers between are  

          

Concept Insight: Since there are infinite number of rational numbers between any two numbers so the answer is not unique here.  The trick is to convert the number to equivalent   form by multiplying and dividing by the number at least 1 more than the rational numbers required.

Alternatively for any two rational numbers a and b,    is also a rational number which lies between a and b.

Question 4.  State whether the following statements are true or false. Give reasons for your answers.

    (i)    Every natural number is a whole number
    (ii)   Every integer is a whole number
    (iii)  Every rational number is a whole number

Solution

(i)    True, since collection of whole numbers contains all natural numbers.
    
(ii)    False, integers include negative of natural numbers as well, which are clearly not whole numbers. For example -1 is an integer but not a whole number.

(iii)    False, rational numbers includes fractions and integers as well. For example  is a rational number but not whole number.

Concept Insight: Key concept involved in this question is the hierarchy of number systems

Remember the bigger set consists of the smaller one.
Since Mathematics is an exact science every fact has a proof but in order to negate a statement even one counter example is sufficient.

Ex-1.2