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Real Numbers is the first chapter of NCERT Maths and forms the foundation for many advanced mathematical concepts. Real numbers include all rational and irrational numbers used in everyday calculations and mathematical operations.

This chapter is important for CBSE Board Exams and Competitive Exams.

What are Real Numbers?

Real numbers are all the numbers that can be represented on a number line.

Types of Real Numbers

  • Natural Numbers
  • Whole Numbers
  • Integers
  • Rational Numbers
  • Irrational Numbers

Together, rational and irrational numbers form the set of real numbers.

Euclid's Division Lemma

Euclid's Division Lemma is a method used to find the Highest Common Factor (HCF) of two positive integers.

It states that for any two positive integers, there exist unique whole numbers that satisfy a specific division relationship.

Chapter - 1: Real Numbers
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Fundamental Theorem of Arithmetic

The theorem states that every composite number can be expressed as a product of prime numbers in a unique way.

This concept is useful in finding:

  • HCF (Highest Common Factor)
  • LCM (Least Common Multiple)

Rational and Irrational Numbers

Rational Numbers

Numbers that can be expressed in the form p/q, where q ≠ 0.

Irrational Numbers

Numbers that cannot be expressed in the form p/q and have non-terminating, non-repeating decimal expansions.

Importance of Real Numbers

  • Forms the basis of algebra and geometry.
  • Helps in solving mathematical equations.
  • Used in measurements and calculations.
  • Essential for higher mathematics.

Importance for CBSE Exams

Real Numbers is a high-scoring chapter in NCERT Maths. Questions are frequently asked on Euclid's Division Lemma, HCF, LCM, prime factorization, rational numbers, and irrational numbers.

Key Topics Covered

  • Real Numbers
  • Euclid's Division Lemma
  • HCF and LCM
  • Prime Factorization
  • Fundamental Theorem of Arithmetic
  • Rational Numbers
  • Irrational Numbers
  • Decimal Expansions
  • Number System
  • Properties of Real Numbers
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