# PSEB 9th Class Maths Solutions Chapter 1 Number Systems Ex 1.1

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 1 Number Systems Ex 1.1 Textbook Exercise Questions and Answers.

## PSEB Solutions for Class 9 Maths Chapter 1 Number Systems Ex 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?
Yes. Zero is a rational number. Zero is a whole number as well as an Integer. As we know, all integers are rational numbers, zero is also a rational number.

Zero can be expressed in the $$\frac{p}{q}$$ form in infinitely many ways like $$\frac{0}{5}$$, $$\frac{0}{11}$$, $$\frac{0}{-3}$$, …….

In short, $$\frac{0}{q}$$, where q is an integer other than zero, is the $$\frac{p}{q}$$ form of 0.

Question 2.
Find six rational numbers between 3 and 4.
Since six rational numbers are to be found. between rationals 3 and 4, we express both of them with denominator 7(6 + 1).
Now, 3 = $$\frac{3 \times 7}{1 \times 7}$$ = $$\frac{21}{7}$$ and 4 = $$\frac{4 \times 7}{1 \times 7}=\frac{28}{7}$$

Then, $$\frac{21}{7}$$ < $$\frac{22}{7}$$ < $$\frac{23}{7}$$ < $$\frac{24}{7}$$ < $$\frac{25}{7}$$ < $$\frac{26}{7}$$ < $$\frac{27}{7}$$ < $$\frac{28}{7}$$ so, $$\frac{22}{7}, \frac{23}{7}, \frac{24}{7}, \frac{25}{7}, \frac{26}{7}, \frac{27}{7}$$ are required six rational numbers between 3 and 4.

By other methods, takIng 3 = 3.0 and 4 = 4.0, we can state that 3.1, 3.2, 3.3, 3.4, 3.5, 3.6 are six rationals between 3 and 4. Still, by the method of averages, we can state $$\frac{7}{2}$$, $$\frac{13}{4}, \frac{15}{4}, \frac{25}{8}, \frac{27}{8}, \frac{29}{8}$$ are six rationals between 3 and 4. As there lies infinitely many rationals between any two rationals, we can give many different answers.

Question 3.
Find five rational numbers between  and .
$$\frac{3}{5}=\frac{3 \times 6}{5 \times 6}=\frac{18}{30}$$ and $$\frac{4}{5}=\frac{4 \times 6}{5 \times 6}=\frac{24}{30}$$
Now, $$\frac{18}{30}$$ < $$\frac{19}{30}$$ < $$\frac{20}{30}$$ < $$\frac{21}{30}$$ < $$\frac{22}{30}$$ < $$\frac{23}{30}$$ < $$\frac{24}{30}$$
i.e., $$\frac{3}{5}$$ < $$\frac{19}{30}$$ < $$\frac{2}{3}$$ < $$\frac{7}{10}$$ < $$\frac{11}{5}$$ < $$\frac{23}{30}$$ < $$\frac{4}{5}$$.
Hence, $$\frac{19}{30}, \frac{2}{3}, \frac{7}{10}, \frac{11}{15}$$ and $$\frac{23}{30}$$ are five of the many rational numbers lying between $$\frac{3}{5}$$ and $$\frac{4}{5}$$.

Question 4.
State whether the following statements are true or false. Give reasons for your answers :
(i) Every natural number is a whole number.
The given statement is true as the collection of whole numbers contain all the natural numbers.

(ii) Every integer is a whole number.
The given statement is false as any negative integer like – 2, – 3, – 5, etc. Is not a whole number. The collection of whole numbers contains 0 and all natural numbers, but not the opposites of the natural numbers.

(iii) Every rational number is a whole number.
The given statement is false as any rational number lying between two consecutive whole numbers is not a whole number.

e.g., $$\frac{5}{2}$$ is a rational number lying between whole numbers 2 and 3, but it is not a whole number.
Skill Testing Exercise