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TEXTBOOK QUESTIONS SOLVED

Exercise 1.1

1. Is zero a rational number? Can you write it in the form ${p \over q}$ , where p and q are integers and q ≠ 0?

Sol. Yes, zero is a rational number as 0 = ${0 \over 1}or{0 \over 2}or{0 \over { - 1}}$.
This is in the form ${p \over q}$, q # 0.

2. Find six rational numbers between 3 and 4.

Sol.
For six rational numbers between 3 and 4,
$3 = {{21} \over 7}and4 = {{28} \over 7}$
Six rational numbers between 3 and 4 are  ${{22} \over 7},{{23} \over 7},{{24} \over 7},{{25} \over 7},{{26} \over 7},{{27} \over 7}$ or another set is 3.1, 3.2, 3.3, 3.4, 3.5, 3.6. There can be.other set of rational numbers also.

3. Find five rational numbers between  ${3 \over 5}and{4 \over 5}$

Sol.
We have ${3 \over 5} = {{18} \over {30}}and{4 \over 5} = {{24} \over {30}}$

Five rational numbers between  ${3 \over 5}and{4 \over 5}are{{19} \over {30}},{{20} \over {30}},{{21} \over {30}},{{22} \over {30}},{{23} \over {30}}.$  There can be other set of rational numbers also.

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.

(iii) False, as ${2 \over 3}$ is a rational number but not a whole number.