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.