NCERT Solutions Class 9 Chapter 1 Number System : Exercise 1.1

The NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.1 provide clear, accurate solutions to these problems in a way that makes the concepts easier to understand. The solutions here are curated by subject experts at Allen, according to the latest CBSE Syllabus, and also explain textbook problems clearly while strengthening your logical thinking and problem-solving skills.

1.0Download NCERT Solutions Class 9 Maths Chapter 1 Exercise 1.1 : Free PDF

The Number System forms an essential basis for mathematical skills and knowledge. The Class 9 Maths Chapter 1 acts as a foundation for many topics you will cover in later classes.

Exercise 1.1 of the NCERT Solutions for Class 9 Maths Chapter 1 contains questions that help students understand essential concepts such as 

• Irrational numbers
• Real numbers
• Representation of these on the number line. 

2.0NCERT Solutions Class 9 Chapter 1 Number Systems: All Exercises

3.0NCERT Class 9 Chapter 1 Number System Exercise 1.1 : Detailed Solutions

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

Sol. Yes, zero is a rational number. We can write zero in the form p/q where p and q are integers and q≠0.

So, 0 can be written as 0/1 = 0/2 = 0/3 etc.

2. Find six rational numbers between 3 and 4.

Sol. First rational number between 3 and 4 is (3+4)/2 = 7/2.

Similarly, other numbers are:

(3+7/2)/2 = (13/2)/2 = 13/4

(3+13/4)/2 = (25/4)/2 = 25/8

(3+25/8)/2 = (49/8)/2 = 49/16

(3+49/16)/2 = (97/16)/2 = 97/32

(97/32+3)/2 = (193/32)/2 = 193/64

So, numbers are 7/2, 13/4, 25/8, 49/16, 97/32, 193/64.

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

Sol. To find rational numbers between 3/5 and 4/5, we can multiply the numerator and denominator by (n+1), where n is the number of rational numbers we want to find (here, n=5). So, n+1=6.

(3/5) × (6/6) = 18/30

(4/5) × (6/6) = 24/30

So, required rational numbers are 19/30, 20/30, 21/30, 22/30, 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.

Sol. (i) True, the collection of whole numbers contains all natural numbers (Whole numbers = {0, 1, 2, 3, ...}, Natural numbers = {1, 2, 3, ...}).

(ii) False, -2 is an integer but it is not a whole number. (Integers = {..., -2, -1, 0, 1, 2, ...})

(iii) False, 1/2 is a rational number but not a whole number. (Rational numbers include fractions).

4.0Key Features and Benefits Class 9 Maths Chapter 1 Number System: Exercise 1.1

• NCERT Solutions adhere to the latest CBSE guidelines and exam patterns.
• Each answer includes clear, logical steps for better conceptual clarity.
• Core concepts according to the CBSE curriculum are concentrated upon.
• Builds a solid base for algebra, geometry, and higher-level math topics.
• These solutions help students prepare effectively for class tests and the CBSE exam.
• Practising NCERT Solutions makes tricky questions more approachable, improving student self-assurance in math.