Real Numbers

This chapter builds the foundation of the real number system for Class 10. It covers Euclid's Division Lemma and Algorithm (retained by many State Boards) for finding HCF, the Fundamental Theorem of Arithmetic and its use in finding HCF and LCM by prime factorisation, proofs of irrationality of numbers like $\sqrt{2}$, $\sqrt{3}$ and $\sqrt{5}$, and the decimal expansions of rational numbers (terminating versus non-terminating recurring). It is a high-scoring, proof-and-numerical chapter that is important for both CBSE and State Board examinations.