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Exercise - 1.1

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

Solution :-
 Yes. Zero is a rational number as it can be represented as 0/1 or 0/2 etc. 
    

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

Solution :-
 We write the 3 and 4 as rational no. with multiply and divide by 1+6=7 then we find that
 3=21/7 and 4=28/7. Now six rational no. in between 21/7 and 28/7 are
 22/7, 23/7, 24/7, 25/7, 26/7, 27/7
    

Question-3 :-  Find five rational numbers between 3/5 and 4/5.

Solution :-
 We write the 3/5 and 4/5 as rational no. with multiply and divide by 1+5=6 then we find that
 3/5=18/30 and 4/5=24/30. Now five rational no. in between 18/30 and 24/30 are
 19/30, 20/30, 21/30, 22/30, 23/30 
    

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 the collection of whole numbers contains all natural numbers.
      e.g. 1 is a whole no. as well as natural no.   
(ii)  False; as integers may be negative but whole numbers are positive. 
      e.g. −5 is an integer but not a whole no.   
(iii) False; as rational numbers may be fractional but whole numbers may not be.
      e.g. 1/2 is a rational no. but not a whole no. 
    
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