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NCERT Solutions
Class 9
Maths
Chapter 1 Number System
Exercise 1.1

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. 

NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.1

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

NCERT Solutions for Class 9 Maths Chapter 1: Exercise 1.1

NCERT Solutions for Class 9 Maths Chapter 1: Exercise 1.2

NCERT Solutions for Class 9 Maths Chapter 1: Exercise 1.3

NCERT Solutions for Class 9 Maths Chapter 1: Exercise 1.4

NCERT Solutions for Class 9 Maths Chapter 1: Exercise 1.5

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.

NCERT Class 9 Maths Ch. 1 Number System Other Exercises:-

Exercise 1.1

Exercise 1.2

Exercise 1.3

Exercise 1.4

Exercise 1.5


NCERT Solutions for Class 9 Maths Other Chapters:-

Chapter 1: Number Systems

Chapter 2: Polynomials

Chapter 3: Coordinate Geometry

Chapter 4: Linear Equations in Two Variables

Chapter 5: Introduction to Euclid’s Geometry

Chapter 6: Lines and Angles

Chapter 7: Triangles

Chapter 8: Quadrilaterals

Chapter 9: Circles

Chapter 10: Heron’s Formula

Chapter 11: Surface Areas and Volumes

Chapter 12: Statistics

Frequently Asked Questions

Irrational numbers do not exist as simple fractions and have non-terminating non-repeating decimal representations.

Examples of irrational numbers, we use values like √2 and √3.

Proof by contradiction is commonly used to show that the number cannot equal any fraction.

Rational numbers represented as decimals are either terminating or repeating, while irrational numbers have non-repeating.

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