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Exercise - 1.1

Number Systems

**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?

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.

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.

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.

(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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