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?

Answer:

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.

Answer:

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 \(\).

Answer:

\(\frac{3}{5}=\frac{3 \times 6}{5 \times 6}=\frac{18}{30}\) 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.

Answer:

The given statement is true as the collection of whole numbers contain all the natural numbers.

(ii) Every integer is a whole number.

Answer:

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.

Answer:

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