Chapter-1 Number Systems

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             Ch. 1 NUMBER SYSTEMS

EXERCISE 1.1


Q1. Is zero a rational number? Can you write it in the form p/q, where p and q are integers and q ≠ 0?

A1. Yes 0 is a rational number. It can be written in the form p/q, where p and q are integers and q≠0. For example, 0/5 where p=0 and q=5.

Q2. Find six rational numbers between 3 and 4.

A2.  ∙3= 30/10,
        ∙4= 40/10
∴ Six rational numbers between 3 and 4 are 31/10, 32/10, 33/10, 34/10, 35/10, 36/10.

Q3. Find five rational numbers between 3/5 and 4/5 .

A3. ∙3/5 = 30/50,
       ∙4/5 = 40/50
∴ Five rational numbers between 3/5 and 4/5 are 31/50, 32/50, 33/50, 34/50, 35/50.

 Q4. 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.

A4. (i) True. Whole numbers include natural numbers( 1, 2, 3...) and 0.
       (ii) False. Integers include negative numbers also which are not whole numbers, for example -8 is a negative integer but not a whole number.
       (iii) False. Rational numbers include fractions too, which are not whole numbers. Example 3/7.
                                         

EXERCISE 1.2

Q1. State whether the following statements are true or false. Justify your answers.
       (i) Every irrational number is a real number.
       (ii)Every point on the number line is of the form √m, where m is a natural number.
       (iii) Every real number is an irrational number. 



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