Haryana State Board HBSE 9th Class Maths Solutions Chapter 1 Number Systems Ex 1.1 Textbook Exercise Questions and Answers.
Haryana Board 9th Class 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?
Solution :
Yes, zero is a rational number.
Yes, it can be written in the form \(\frac {p}{q}\) as follows:
\(\frac{0}{1}=\frac{0}{2}=\frac{0}{3}\) etc., denominator q can also be taken as negative integer.
Question 2.
Find six rational numbers between 3 and 4.
Solution:
To find six rational numbers between 3 and 4, we write rational numbers 3 and 4 with denominator 7(6 + 1) as follows:
3 = \(\frac{3 \times 7}{7}=\frac{21}{7}\)
4 = \(\frac{4 \times 7}{7}=\frac{28}{7}\)
Six rational numbers between 3 and 4 are
\(\frac{22}{7}, \frac{23}{7}, \frac{24}{7}, \frac{25}{7}, \frac{26}{7}\) and \(\frac {27}{7 }\)
Hence, six rational numbers between 3 and 4 are
\(\frac{22}{7}, \frac{23}{7}, \frac{24}{7}, \frac{25}{7}, \frac{26}{7}\) and \(\frac {27}{7 }\)
Question 3.
Find five rational numbers between \(\frac {3}{5}\) and \(\frac {4}{5}\)
Solution:
To find 5 rational numbers between \(\frac {3}{5}\) and \(\frac {4}{5}\), we multiply the numerator and denominator of \(\frac {3}{5}\) and \(\frac {4}{5}\) by 6(5 + 1).
\(\frac{3}{5}=\frac{3 \times 6}{5 \times 6}=\frac{18}{30}\)
\(\frac{4}{5}=\frac{4 \times 6}{5 \times 6}=\frac{24}{30}\)
Five rational numbers between \(\frac {3}{5}\) and \(\frac {4}{5}\) are :
\(\frac{19}{30}, \frac{20}{30}, \frac{21}{30}, \frac{22}{30}\) and \(\frac {23}{30}\)
Hence, five rational numbers between \(\frac {3}{5}\) and \(\frac {4}{5}\) are :
\(\frac{19}{30}, \frac{20}{30}, \frac{21}{30}, \frac{22}{30}\) and \(\frac {23}{30}\)
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.
Solution :
(i) True, since the collection of the whole numbers contains all the natural numbers.
(ii) False, since negative integers are not whole numbers.
(iii) False, since \(\frac {2}{5}\) is a rational number but not a whole number.