Rajasthan Board RBSE Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.1 Textbook Exercise Questions and Answers.

## RBSE Class 9 Maths Solutions Chapter 1 Number Systems Exercise 1.1

Question 1.

Is zero a rational number? Can you write it in the form where p and q are integers and q ≠ 0?

Answer:

Yes, 0 is a rational number.

0 can be written in any of the following forms :

\(\frac{0}{1}, \frac{0}{-2}, \frac{0}{3}, \frac{0}{-4}\) and so on. .

Thus, 0 can be written as \(\frac{p}{q}\), where p = 0 and q is any non-zero integer.

Hence, 0 is a rational number.

Question 2.

Find six rational numbers between 3 and 4.

Answer:

We know that between two rational numbers a and b, such that a < b.

There is always a rational number \(\frac{a+b}{2}\), where a < \(\frac{a+b}{2}\) < b.

A rational number between 3 and 4 is \(\frac{1}{2}\)(3 + 4), i.e. \(\frac{7}{2}\).

Hence, six rational numbers between 3 and \(\frac{13}{4}\) are:

\(\frac{25}{8}, \frac{13}{4}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}\) and \(\frac{63}{16}\).

Aliter: There can be infinitely many rational numbers between the numbers 3 and 4, one way is to multiply and divide by 6 + 1 = 7, to get an equivalent fraction like :

3 × \(\frac{7}{7}\) = \(\frac{21}{7}\).

4 × \(\frac{7}{7}\) = \(\frac{28}{7}\).

We know that 21 < 22 < 23 < 24 < 25 < 26 < 27 < 28

⇒ \(\frac{21}{7}<\frac{22}{7}<\frac{23}{7}<\frac{24}{7}<\frac{25}{7}<\frac{26}{7}<\frac{27}{7}<\frac{28}{7}\)

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 \(\frac{4}{5}\).

Answer:

Since, we want 5 rational numbers between \(\frac{3}{5}\) and \(\frac{4}{5}\), so we write:

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:

True: Since the collection of whole numbers contains all the natural numbers.

(ii) Every integer is a whole number.

Answer:

False: – 2 is not a whole number.

(iii) Every rational number is a whole number.

Answer:

False: \(\frac{2}{7}\) is a rational number but it is not a whole number.

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