Skip to main content
Super TutorResources
Chapter 1 of 16
Chapter Summary

Real Numbers — Chapter Summary

Madhya Pradesh Board · Class 10 · Mathematics

Summary of Real Numbers for Madhya Pradesh Board Class 10 Mathematics. Part of the Madhya Pradesh Board Class 10 Mathematics syllabus.

116 questions50 flashcards11 formulas & key relations5 concepts

Interactive on Super Tutor

Studying Real Numbers? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for chapter summary and more.

Try Super Tutor — Free

Free trial, no card needed.

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).
Super Tutor

One of 6 illustrations for Real Numbers in Super Tutor — alongside flashcards, concept maps and practice questions.

Overview

Real numbers include rational and irrational numbers. The chapter connects number theory and decimal expansions through Euclid's division algorithm, the Fundamental Theorem of Arithmetic, and basic results on irrational numbers. It also shows how prime factorisation helps in finding HCF and LCM, and

Key Concepts

For any two positive integers

For any two positive integers a and b, a can be written as a = bq + r, where 0 is less than or equal to r and r is smaller than b. It is mainly used t

Every composite number can be expressed

Every composite number can be expressed as a product of primes, and this factorisation is unique apart from the order of the prime factors.

A composite number x can be

A composite number x can be written as x = p1 p2 ... pn, where the primes are listed in ascending order. Combining equal primes gives powers of primes

The HCF of two or more

The HCF of two or more numbers is the product of the smallest power of each common prime factor.

The LCM is the product

The LCM is the product of the greatest power of each prime factor involved in the numbers.

Learning Objectives

  • Understand Euclid's division algorithm and its use in finding HCF.
  • State and use the Fundamental Theorem of Arithmetic.
  • Write composite numbers as products of prime factors in ascending order.
  • Find HCF and LCM by prime factorisation.
  • Use prime factorisation to study decimal expansions of rational numbers.

Frequently Asked Questions

What are the important topics in Real Numbers for Madhya Pradesh Board Class 10 Mathematics?
Key topics in Real Numbers include Euclid's Division Algorithm, Fundamental Theorem of Arithmetic, HCF and LCM by Prime Factorisation, Irrational Numbers and Irrationality Proofs. Study these first, then practise questions on each for the Madhya Pradesh Board Class 10 board exam.
How should I revise Real Numbers for the Madhya Pradesh Board Class 10 board exam?
Learn the core ideas first, then work through the 116 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 Madhya Pradesh Board Class 10 Mathematics Chapter Summary

For serious students

Get the full Real Numbers chapter — start free.

Quizzes, flashcards, an AI doubt solver and a study plan for Madhya Pradesh Board Class 10 Mathematics. Free to start, no card needed.

Try Super Tutor Free
Try this chapter free