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Real Numbers — Revision Notes

Telangana Board · Class 10 · Mathematics

Real Numbers revision notes for Telangana Board Class 10 Mathematics: 4 topics in quick points. Part of the Telangana Board Class 10 Mathematics syllabus.

43 questions28 flashcards10 formulas & key relations5 concepts

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Key Topics to Revise

1

Division Algorithm and Euclid's Algorithm

  • For positive integers a and b, there exist unique whole numbers q and r such that a = bq + r and 0 ≤ r < b.
  • This result is called the Division Algorithm.
  • The Division Algorithm is different from Euclid's algorithm, although they are closely related.
2

Prime Factorisation, HCF and LCM

  • The Fundamental Theorem of Arithmetic states that every composite number can be expressed as a product of primes and this factorisation is unique apart from the order of the prime factors.
  • Every composite number has a prime factorisation.
  • For 24, the prime factorisation is 2 × 2 × 2 × 3.
3

Decimal Expansions of Rational Numbers

  • A rational number has either a terminating decimal expansion or a non-terminating repeating decimal expansion.
  • A terminating decimal can be written in simplest p/q form where the denominator has only prime factors 2 and/or 5.
  • If q has prime factorisation of the form 2^n 5^m, then the decimal expansion terminates.
4

Irrational Numbers and Proofs

  • A real number is irrational if it cannot be written as p/q, where p and q are integers and q ≠ 0.
  • Examples of irrational numbers include √2, √3, √15, π, and 0.10110111011110....
  • Theorem 1.6 states: if p is prime and p divides a^2, then p divides a.

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Full Notes

Key Concepts

For positive integers a and bThis is a stepwise methodEvery composite number can be expressedHCF is the greatest positive integerA rational number in simplest form

Frequently Asked Questions

What are the important topics in Real Numbers for Telangana Board Class 10 Mathematics?
Key topics in Real Numbers include Division Algorithm and Euclid's Algorithm, Prime Factorisation, HCF and LCM, Decimal Expansions of Rational Numbers, Irrational Numbers and Proofs. Study these first, then practise questions on each for the Telangana Board Class 10 board exam.
How should I revise Real Numbers for the Telangana Board Class 10 board exam?
Learn the core ideas first, then work through the 43 practice questions on Real Numbers. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

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

More resources for Real Numbers

All Telangana Board Class 10 Mathematics Revision Notes

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