NCERT Solutions Class 9 Maths Chapter 1 Number Systems Ex 1.1

NCERT Solutions Class 9 Maths
Chapter – 1 (Number Systems )

The NCERT Solutions in English Language for Class 9 Mathematics Chapter – 1 Number Systems Exercise 1.1 has been provided here to help the students in solving the questions from this exercise.

Chapter 1: Number Systems

Exercise – 1.1

1. Is zero a rational number? Can you write it in the form $\mathbf{\frac{p}{q}}$ where p and q are integers and q ≠ 0?
Answer – Yes, write $\frac{0}{1}$ (where 0 and 1 are integers and q = 1 which is not equal to zero).

2. Find six rational numbers between 3 and 4.
Answer – There are infinite rational numbers between 3 and 4.
⇒ $\frac{3}{1}$ and $\frac{4}{1}$
Multiply and division both the side by 7. (n + 1 = 6 + 1 = 7)
i.e., 3 × $\frac{7}{7}$ = $\frac{21}{7}$ and, 4 × $\frac{7}{7}$ = $\frac{28}{7}$
Therefore,
Six rational numbers between 3 and 4 are:
$\frac{22}{7}, \frac{23}{7}, \frac{24}{7}, \frac{25}{7}, \frac{26}{7}$ and $\frac{27}{7}$

$\frac{22}{7}, \frac{23}{7}, \frac{24}{7}, \frac{25}{7} \frac{26}{7} a n d \frac{27}{7}$ 3. Find five rational numbers between $\mathbf{\frac{3}{5}}$ and $\mathbf{\frac{4}{5}}$ .
Answer – There are infinite rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$ .
Multiply and division both the side by 6. (n + 1 = 5 + 1 = 6)
i.e., $\frac{3}{5}$ × $\frac{6}{6}$ = $\frac{18}{30}$ and, $\frac{4}{5}$ × $\frac{6}{6}$ = $\frac{24}{30}$

Therefore,
Six rational numbers between $\frac{3}{5}$ or $\frac{18}{30}$ and $\frac{4}{5}$ or $\frac{24}{30}$ are:
$\frac{19}{30},\frac{20}{30},\frac{21}{30},\frac{22}{30}$ and $\frac{23}{30}$ .

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.
Answer –
(i) Every natural number is a whole number. (True)
Because natural numbers are 1, 2, 3, 4 ………., ∞ and whole numbers are 0, 1, 2, 3, 4, 5, ……..,∞.
The collection of whole numbers contain all the natural numbers.

(ii) Every integer is a whole number. (False)
∵ negative integers are not included in the list of whole numbers.

(iii) Every rational number is a whole number. (False)
∵ $\frac{1}{2},\frac{3}{4},\frac{10}{11}$ are not whole numbers.

NCERT Solutions Class 9 Maths Chapter 1 Number Systems Ex 1.1