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

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(Last Updated On: April 9, 2023)

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.1 are part of the NCERT Solutions for Class 9 Maths. Here we have given the NCERT Solutions for Class 9 Maths Chapter 1 Number System Ex 1.1.

## NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.1

### Exercise 1.1 Page: 5

#### Ex 1.1 Class 9 Maths Question 1.

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

Solution:

Yes, zero is a rational number which can be written in the form pq where p and q are integers and q ≠0.
0/1 = 0 ,0/2 = 0,  0/3=0  etc. The denominator q can also be taken as a negative integer.

Taking the case of ‘0’,

We may infer that 0 can be represented in the form p/q, where q may be either a positive or a negative number, because it meets the necessary requirement.

Hence 0 is a rational number.

Also See:

#### Ex 1.1 Class 9 Maths Question 2.

Find six rational numbers between 3 and 4.

Solution:

Let’s say that qi is a rational number between 3
and 4, where j = 1 to 6. Or you can say that there are infinite number of rational numbers between 3 and 4.
The following are the six rational numbers:

Multiplying both 3 and 4 by 6+1 = 7 will help us find 6 rational numbers between 3 and 4. (or any number greater than 6).

That is, 3 × (7/7) = 21/7

And, 4 × (7/7) = 28/7. The numbers between 21/7 and 28/7 will be rational and between 3 and 4.

Between 22/7, 23/7, 24/7, 25/7, 26/7, 27/7, 3 and 4, there are six rational numbers.

#### Ex 1.1 Class 9 Maths Question 3.

Find five rational numbers between 3/5 and 4/5.

Solution:

There are infinite number of rational numbers between 3/5 and 4/5.

We multiply both 3/5 and 4/5 by 5 to discover 5 rational values between 3/5 and 4/5.

with 5+1=6 (or any number greater than 5)

Since we need to find five rational numbers, multiply the numerator and denominator by 6.

That is, (3/5) × (6/6) = 18/30

And, (4/5) × (6/6) = 24/30

Numbers between 18/30 and 24/30 will be rational and between 3/5 and 4/5.

Therefore, the five rational numbers 19/30, 20/30, 21/30, 22/30, and 23/30 are between 3/5 and 4/5.

#### Ex 1.1 Class 9 Maths Question 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.

Solution:

(i) True
The collection of all natural numbers and 0’s are called whole numbers.
(ii) False
Negative integers are not whole numbers.
(iii) False
Rational numbers p/q are of the form q 0 and q does not exactly divide p which are not whole numbers.

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