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Real Numbers

Madhya Pradesh Board · Class 10 · Mathematics

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

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A Venn diagram illustrating the classification of real numbers into rational and irrational numbers, with further subdivisions for rational numbers (integers, whole numbers, natural numbers).
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Key Topics to Revise

1

Euclid's Division Algorithm

  • Euclid's division algorithm is used mainly to compute the HCF of two positive integers.
  • It states that any positive integer a can be divided by another positive integer b in such a way that it leaves a remainder r that is smaller than b.
  • This is the usual long division process.
2

Fundamental Theorem of Arithmetic

  • Every composite number can be expressed as a product of primes, and this factorisation is unique apart from the order in which the prime factors occur.
  • The theorem concerns composite numbers, not prime numbers.
  • Prime factorisation is written in ascending order when a number is expressed as a product of primes.
3

HCF and LCM by Prime Factorisation

  • The HCF of two numbers is found by taking the smallest power of each common prime factor.
  • The LCM of two numbers is found by taking the greatest power of each prime factor involved.
  • For two positive integers a and b, HCF(a, b) x LCM(a, b) = a x b.
4

Irrational Numbers and Irrationality Proofs

  • A number s is irrational if it cannot be written in the form p/q, where p and q are integers and q is not zero.
  • Examples of irrational numbers include square root of 2, square root of 3, square root of 15, pi, minus square root of 2 divided by square root of 3, and 0.10110111011110...
  • The Fundamental Theorem of Arithmetic is used to prove irrationality of square root of 2, square root of 3 and square root of 5.

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Full Notes

Key Concepts

For any two positive integersEvery composite number can be expressedA composite number x can beThe HCF of two or moreThe LCM is the product

Frequently Asked Questions

What are the important topics in Real Numbers for Madhya Pradesh Board Class 10 Mathematics?
Key topics in Real Numbers include How to Correctly Identify Rational vs Irrational Numbers, Real Numbers Chapter — Complete Concept Map, Real Numbers — Complete Chapter Overview. These are the concepts Madhya Pradesh Board Class 10 examiners draw on most — study them first, then practise related questions.
How to score full marks in Real Numbers — Madhya Pradesh Board Class 10 Mathematics?
Understand the core concepts first, then work through the 116 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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