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Real Numbers

Telangana Board · Class 10 · Mathematics

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

45 questions28 flashcards5 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?
Real Numbers covers several key topics that are frequently asked in Telangana Board Class 10 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Real Numbers — Telangana Board Class 10 Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and 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.

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All 14 chapters — Telangana Board Class 10 Mathematics Revision Notes

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