Unit 1: Real Numbers

Overview

Real Numbers is the first chapter in the CBSE Class 10 Mathematics syllabus. This chapter covers important concepts that lay the foundation for higher mathematical studies. You will learn about the properties of real numbers, Euclid’s Division Lemma, and the Fundamental Theorem of Arithmetic. This unit also introduces important concepts related to rational and irrational numbers.

Topics Covered

1. Introduction to Real Numbers
   • Definition and examples
   • Types of real numbers (Natural numbers, Whole numbers, Integers, Rational, and Irrational numbers)
2. Euclid’s Division Lemma
   • Explanation of Euclid’s Division Lemma
   • Step-by-step method for applying the lemma to find the Highest Common Factor (HCF)
3. The Fundamental Theorem of Arithmetic
   • Prime factorization method
   • Unique factorization of integers
   • Examples of finding prime factors
4. Decimal Expansions of Rational Numbers
   • Recurring and non-recurring decimal expansions
   • Representation of rational and irrational numbers on the number line
5. LCM and HCF
   • Relationship between LCM and HCF
   • Applications of LCM and HCF in solving problems

Key Formulas and Concepts

• Euclid’s Division Lemma: If $a$ and $b$ are two positive integers, then there exist unique integers $q$ and $r$, such that $a=bq+r$, where $0\le r<b$.
• Fundamental Theorem of Arithmetic: Every composite number can be expressed as a product of prime numbers in a unique way, except for the order of the primes.
• LCM and HCF relationship: