CBSE Notes Class 9 Maths Chapter 3 - The World of Numbers
CBSE Class 9 Maths Notes Chapter 3 - The World of Numbers are prepared according to the latest CBSE syllabus 2026-27 and the revised NCERT textbook, Ganita Manjari. These notes help students understand key concepts in a simple and structured way, making it easier to revise important topics, definitions, solved examples, and key points before class tests and annual examinations. They are also helpful for completing homework, practising concepts, and preparing effectively for exams.
The chapter "The World of Numbers" introduces students to the fundamental concepts of rational numbers, irrational numbers, and real numbers. Students learn about decimal forms of real numbers and their representation on the number line. The chapter further covers recurring decimals, finding numbers between two numbers, operations on real numbers, surds, and square-root identities. These concepts help students develop a deeper understanding of the number system and provide a strong foundation for higher-level mathematical concepts.
1.0Download CBSE Notes Class 9 Maths Chapter 3 - The World of Numbers
These Class 9 Maths Chapter 3 notes cover the main topics of the number system in one place. Students can use them to revise rational and irrational numbers, decimal expansions, number-line representation, and important rules.
2.0Important Concepts Class 9 Maths Chapter 3 - The World of Numbers
Rational Numbers
A rational number is a number that can be written as p/q, where p and q are integers and q is not zero. Examples include 3/4, -7/9, 0, and 2. Every rational number can be marked at a definite point on the number line.
Rational Numbers Between Two Numbers
There are infinitely many rational numbers between any two different rational numbers. More rational numbers can be found by writing equivalent fractions or using a suitable method.
Decimal Expansion of Rational Numbers
Rational numbers can have two types of decimal expansions:
- Terminating decimal: The decimal ends after a fixed number of digits. For example, 3/4 = 0.75.
- Non-terminating repeating decimal: A digit or group of digits keeps repeating. For example, 5/3 = 1.666....
Recurring Decimals in p/q Form
A recurring decimal can be changed into the form p/q.
- Pure recurring decimal: The digits start repeating immediately after the decimal point.
- Mixed recurring decimal: Some digits come before the repeating digits.
The conversion can be done by multiplying the decimal by suitable powers of 10 and subtracting the original equation.
Irrational Numbers
An irrational number cannot be written in the form p/q, where p and q are integers and q is not zero. Its decimal form goes on without ending and does not have a repeating pattern.
Examples include √2, √3, and π.
Real Numbers
Rational numbers and irrational numbers together make up the set of real numbers. Every real number can be shown by a point on the real number line.
Representation of Irrational Numbers on the Number Line
Irrational numbers such as √2, √3, and √5 can be shown on the number line with the help of right-angled triangles and the Pythagoras theorem. A square root spiral can also be used to mark square roots on the number line.
Operations on Real Numbers
Some important results are:
- The negative of an irrational number is irrational.
- The sum of a rational number and an irrational number is irrational.
- The difference between a rational number and an irrational number is irrational.
- The product of a non-zero rational number and an irrational number is irrational.
- Adding, subtracting, multiplying, or dividing two irrational numbers can give either a rational or an irrational number.
Important Radical Identities
For positive real numbers a and b:
√ab = √a × √b
√(a/b) = √a / √b
(√a + √b)(√a − √b) = a − b
(√a + √b)² = a + 2√ab + b
A number containing a root that cannot be written as a rational number is called a surd.
3.0Other Study Materials for Class 9 Maths
Students can use additional study materials along with these notes, such as:
4.0Why CBSE Notes Class 9 Maths - The World of Numbers
These notes bring the main points of the chapter together, making it easier for students to study and revise.
- Save study time: Find the main points in one place.
- Check your understanding: Read the topics before solving exercises.
- Support self-study: Use the notes while studying the chapter on your own.
- Revise before tests: Go through important points before a test or exam.
- Improve accuracy: Check rules and steps while practising questions.