These NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.1 Questions and Answers are prepared by our highly skilled subject experts.
NCERT Solutions for Class 9 Maths 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?
Solution:
Yes, zero is a rational number. Because, \(\frac{0}{i}\) is also equal to zero. Where is integer. Zero is also represented by \(\frac{0}{1}\), which is in the form of \(\frac{p}{q}\), where p and q both are integers and q ≠ 0.
Question 2.
Find six rational numbers between 3 and 4.
Solution:
To find six rational number between 3 and 4, we take 3 and 4 as a rational number with denominator 6 + 1 = 7, i.e.
3 = \(\frac{21}{7}\) and 4 = \(\frac{28}{7}\)
Then required six rational number between 3 and 4 are
\(\frac{22}{7}, \frac{23}{7}, \frac{24}{7}, \frac{25}{7}, \frac{26}{7} \text { and } \frac{27}{7}\)
Question 3.
Find five rational numbers between \(\frac{3}{5}\) and \(\frac{4}{5}\).
Solution:
To find five rational numbers between \(\frac{3}{5}\) and \(\frac{4}{5}\), we take \(\frac{3}{5}\) and \(\frac{4}{5}\) as a rational number with denominator 30.
i.e. \(\frac{3}{5}=\frac{3}{5} \times \frac{6}{6}=\frac{18}{30}\) and \(\frac{4}{5}=\frac{4}{5} \times \frac{6}{6}=\frac{24}{30}\)
Then, required six rational numbers between \(\frac{3}{5}\) and \(\frac{4}{5}\) are
\(\frac{19}{30}, \frac{20}{30}, \frac{21}{30}, \frac{22}{30} \text { and } \frac{23}{30}\)
Question 4.
State whether the following statements are true or false? Give a reason for your answer.
(i) Every natural number is a whole number.
(ii) Every integer is a whole number.
(iii) Every rational number is a whole number.
Solution:
(i) True, because numbers 1, 2, 3, 4, 5, ………. is a natural number and whole number is 0, 1, 2, 3, 4, 5, ………
(ii) False, because -1 is an integer but it is not a whole number.
(iii) False, because \(\frac{1}{2}\) is a rational number but it is not a whole number.