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.