JAC Class 9 Maths Solutions Chapter 1 Number Systems Ex 1.1

Jharkhand Board JAC Class 9 Maths Solutions Chapter 1 Number Systems Ex 1.1 Textbook Exercise Questions and Answers.

JAC Board Class 9th Maths Solutions Chapter 1 Number Systems Exercise 1.1

Question 1.
Is zero a rational number? Can you write it in the form $$\frac{p}{q}$$, where p and q are integers and q ≠ 0?
Answer:
Yes, Zero is a rational number as it can be represented as $$\frac{0}{1}$$ or $$\frac{0}{2}$$ and so on.

Question 2.
Find six rational numbers between 3 and 4.
Answer:
There are infinitely many rational numbers between 3 and 4.
3 and 4 can be represented as $$\frac{24}{8}$$ and $$\frac{32}{8}$$ respectively.
Therefore, six rational numbers between 3 and 4 are: $$\frac{25}{8}$$, $$\frac{26}{8}$$, $$\frac{27}{8}$$, $$\frac{28}{8}$$, $$\frac{29}{8}$$, $$\frac{30}{8}$$.

Question 3.
Find five rational numbers between $$\frac{3}{5}$$ and $$\frac{4}{5}$$.
Answer:
There are infinitely many rational numbers between $$\frac{3}{5}$$ and $$\frac{4}{5}$$
$$\frac{3}{5}=\frac{3 \times 6}{5 \times 6}=\frac{18}{30}$$
$$\frac{4}{5}=\frac{4 \times 6}{5 \times 6}=\frac{24}{30}$$
Therefore, five rational numbers between $$\frac{3}{5}$$ and $$\frac{4}{5}$$ are $$\frac{19}{30}$$, $$\frac{20}{30}$$, $$\frac{21}{30}$$, $$\frac{22}{30}$$, $$\frac{23}{30}$$.

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.
Answer:
(i) True, since the collection of whole numbers contains all natural numbers.
(ii) False, as integers may be negative but whole numbers are always positive, e.g. – 1 is an integer but not a whole number.
(iii) False, as rational numbers may be fractional but whole numbers are not fractional, e.g. $$\frac{2}{3}$$ is a rational number but not a whole number.