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Real Numbers

Kerala Board · Class 10 · Mathematics

Quick revision notes for Real Numbers — Kerala Board Class 10 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

45 questions22 flashcards5 concepts

Key Topics to Revise

1

Division Algorithm

  • For any two positive integers a and b, there exist unique whole numbers q and r such that a = bq + r, where 0 ≤ r < b
  • a is the dividend, b is the divisor, q is the quotient, and r is the remainder
  • This algorithm is the foundation for Euclid's algorithm to find HCF
2

Euclid's Algorithm for HCF

  • Euclid's algorithm is based on the principle that HCF(c,d) = HCF(d,r) where c = dq + r
  • Continue applying division algorithm until remainder becomes zero
  • The last non-zero remainder is the HCF
3

Fundamental Theorem of Arithmetic

  • Every composite number can be expressed as a product of primes
  • This factorization is unique, apart from the order of prime factors
  • Used to find HCF and LCM using prime factorization method
4

Rational Numbers and Decimal Expansions

  • A rational number p/q has terminating decimal if q = 2ⁿ × 5ᵐ (after reducing to lowest terms)
  • A rational number has non-terminating repeating decimal if q has prime factors other than 2 and 5
  • Every terminating decimal can be expressed as p/q where q is a power of 10

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Full Notes

Key Concepts

For positive integers a and bA systematic method to findEvery composite number can be expressedA rational number p/q hasNumbers that cannot be expressed

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Frequently Asked Questions

What are the important topics in Real Numbers for Kerala Board Class 10 Mathematics?

Real Numbers covers several key topics that are frequently asked in Kerala Board Class 10 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.

Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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All 14 chapters — Kerala Board Class 10 Mathematics Revision Notes