Class notes Mathematics NCERT Class 10 Mathematics Solutions
Chapter Overview: Real Numbers This chapter deals with real numbers, their properties, and key number theory concepts. Here's what it includes. 1. Euclid’s Division Lemma Statement: For any two positive integers a and b, there exist unique integers q and r such that: a = bq + r, where 0 ≤ r b Used to find the Highest Common Factor (HCF) of two numbers using the Euclidean Algorithm. 2. Fundamental Theorem of Arithmetic Every composite number can be expressed uniquely (apart from the order) as a product of prime numbers. Important in finding LCM and HCF using prime factorization. 3. Revisiting Irrational Numbers Proofs that √2, √3, √5 are irrational using contradiction method. 4. Rational Numbers and Their Decimal Expansions Rational numbers either have terminating or non-terminating repeating decimals. Criteria: If the prime factorization of the denominator (after simplification) has no prime factors other than 2 or 5, the decimal expansion terminates. Otherwise, it is non-terminating repeating. 5. Practice Questions and Examples Step-by-step solutions on: Applying Euclid’s division algorithm Prime factorization Proving irrationality Identifying types of decimal expansions
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