NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.1 - Number Systems

Q1 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.

We know that any number of the form $\frac{p}{q}$, where p and q are integers and q $\neq$ 0, is a rational number.

Zero can be written as $\frac{0}{1}, \frac{0}{2}, \frac{0}{3}, \dots,$ etc.

Hence, 0 is rational because it satisfies the condition of being in $\frac{p}{q}$ form.

Q2 Find six rational numbers between 3 and 4.

Answer:

There are an infinite number of rational numbers between 3 and 4.
We can find rational numbers between two numbers using the formula:
If $ a < b $, then a rational number between them is $\frac{a + b}{2}$

Let us find six rational numbers between 3 and 4:

Let $a $= 3, $b$ = 4

$x_1 = \frac{3 + 4}{2} = \frac{7}{2} $= 3.5

$x_2 = \frac{3 + 3.5}{2} = \frac{6.5}{2}$ = 3.25

$x_3 = \frac{3 + 3.25}{2} = \frac{6.25}{2}$ = 3.125

$x_4 = \frac{3.5 + 4}{2} = \frac{7.5}{2} $= 3.75

$x_5 = \frac{3.75 + 4}{2} = \frac{7.75}{2}$ = 3.875

$x_6 = \frac{3.5 + 3.75}{2} = \frac{7.25}{2}$ = 3.625

Therefore, six rational numbers between 3 and 4 are:
3.125, 3.25, 3.5, 3.625, 3.75, 3.875

Q3 Find five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$ .

Answer:

First, convert to same denominator:
$\frac{3}{5} = \frac{18}{30}, \frac{4}{5} = \frac{24}{30}$

Thus, five rational numbers between them can be:
$\frac{19}{30}, \frac{20}{30}, \frac{21}{30}, \frac{22}{30}, \frac{23}{30}$

Q4 (i) State whether the following statements are true or false. Give reasons for your answers. (i)Every natural number is a whole number.

Answer:

True,

The number that is starting from 1, i.e 1, 2, 3, 4, 5, 6, .................. are natural numbers

The number that is starting from 0. i.e, 0, 1, 2, 3, 4, 5.............are whole numbers

Therefore, we can clearly see that the collection of whole numbers contains all natural numbers.

Q4 (ii) State whether the following statements are true or false. Give reasons for your answers. (ii) Every integer is a whole number.

Answer:

False,

Integers may be negative or positive but whole numbers are always positive. For eg. -1 is an integer but not a whole number.

Q4 (iii) State whether the following statements are true or false. Give reasons for your answers.(iii) Every rational number is a whole number.

Answer:

False,

We know that any number of the form $\frac{p}{q}$, where p and q are integers and q $\neq$ 0, is a rational number.

And numbers that are starting from 0 i.e. 0,1,2,3,4,......... are whole numbers

Therefore, we can clearly see that every rational number is not a whole number for eg. $\frac{3}{4}$ is a rational number but not a whole number.