Welcome to Real Numbers II, where you will deepen your understanding of rational and irrational numbers and their properties. In this chapter, you will define irrational numbers and learn systematic methods to verify whether a given number is irrational or not using logical reasoning and proofs.

You will also revise and strengthen the concept of rational numbers, with a special focus on their decimal expansions. You will learn how to convert rational numbers into decimal form and identify whether the decimal expansion is terminating or non-terminating recurring. Through clear explanations and solved examples, this chapter builds strong number sense and analytical skills, which are essential for CBSE Board examinations and higher-level mathematics.