Chapter 1 – Real Numbers | Class 10 Mathematics Notes

📘 Chapter 1 Real Numbers

Master Chapter 1 – Real Numbers with comprehensive study notes, video lessons, NCERT solutions, MCQs, PYQs, competency-based questions, formula sheets, and practice worksheets. Everything you need to prepare confidently for the CBSE Class 10 Mathematics exam is available in one place.

Last Updated

Last Updated: July 2026
Based on the latest CBSE 2026–27 syllabus

Table of Contents

What's Included

📹

 Complete Video Lesson

Step-by-step video lessons covering every concept based on the latest CBSE syllabus.

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📄

Study Notes

Comprehensive notes with explanations, solved examples, and important concepts.

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🧠

Mind Map

Visual chapter summary for quick revision of important concepts and formulas.

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📚

 Formula Sheet

Access all important formulas, revision points, and key facts for quick exam preparation.

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📖

 NCERT Solutions

Step-by-step solutions for every NCERT textbook exercise with clear explanations.

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📘

Exemplar Solutions

Detailed solutions for NCERT Exemplar questions to strengthen higher-order thinking.

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 Important Questions

Most expected board exam questions with detailed solutions and explanations.

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🕒

 PYQs

Previous Year Questions to understand the latest CBSE board exam pattern.

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MCQs

Chapter-wise multiple-choice questions for concept reinforcement and quick revision.

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🎯

Competency-Based Questions

Assertion & Reason and Case Study questions based on the latest CBSE pattern.

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📑

 Sample Paper

Full-length CBSE sample papers for practice, speed, and exam confidence.

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✍️

Practice Worksheet

Additional practice questions to improve problem-solving skills and self-assessment.

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About this Chapter

Chapter 1 – Real Numbers is the foundation of Class 10 Mathematics and introduces important concepts that are used throughout higher mathematics. In this chapter, you will learn about Euclid’s Division Lemma, Fundamental Theorem of Arithmetic, prime factorisation, HCF (Highest Common Factor), LCM (Least Common Multiple), and the decimal expansion of rational numbers. You will also understand the difference between rational and irrational numbers and learn how to determine whether the decimal expansion of a rational number is terminating or non-terminating recurring.

This chapter is highly important for the CBSE Class 10 Board Examination, as questions are regularly asked from topics such as HCF & LCM, irrational numbers, Euclid’s Division Lemma, and decimal expansions. A strong understanding of these concepts will also help you in later chapters and competitive examinations.

On this page, you’ll find everything you need to master Chapter 1 in one place, including complete video lessons, detailed study notes, formula sheets, mind maps, NCERT Textbook Solutions, NCERT Exemplar Solutions, Important Questions, Previous Year Questions (PYQs), MCQs, Competency-Based Questions (Assertion & Reason and Case Study Questions), Practice Worksheets, and Sample Papers. These resources are carefully designed according to the latest CBSE syllabus and exam pattern to help you build strong concepts, revise effectively, and prepare confidently for your board examinations.

Learning Outcomes

  • Understand Euclid’s Division Lemma
  • Find HCF and LCM
  • Apply Fundamental Theorem of Arithmetic
  • Distinguish rational and irrational numbers
  • Solve CBSE questions

🎥 Complete Chapter Explanation

📄 Complete Study Notes

Download beautifully designed chapter notes with explanations, solved examples, formulas, and board exam preparation.

🧠 Chapter Mind Map

Revise the complete chapter quickly using this visual mind map.

📐 Formula Sheet

Download all important formulas and revision points for quick exam preparation.

📚 Exam Preparation Resources

Practice chapter-wise questions based on the latest CBSE exam pattern.

⭐  Important Questions

Practice the most important board exam questions with detailed solutions.

CH1 IMP QUES

📚 Previous Year Questions

Practice previous years’ CBSE board questions to understand the latest exam pattern.

✅ Multiple Choice Questions

Revise the chapter with concept-based MCQs prepared according to the latest CBSE syllabus.

🧠 Competency-Based Questions

Strengthen conceptual understanding with competency-based questions aligned with the latest CBSE assessment pattern.

✍ Practice Worksheet

Solve additional practice questions to improve speed, accuracy, and confidence.

📘 NCERT Textbook Solutions

Access step-by-step solutions for all NCERT textbook exercises with clear explanations.

📄 Detailed Study Notes

Download beautifully designed chapter notes with explanations,examples and  formulas.

📗 NCERT Exemplar Solutions

Practice higher-order thinking questions with detailed NCERT Exemplar solutions.

📝 Sample Paper

Practice full-length CBSE sample papers designed according to the latest exam pattern to improve accuracy, time management, and exam confidence.

⚡ Quick Revision

📄

Formula Sheets

Quick revision formulas

🧠

Mind Maps

Visual chapter summaries

📝

Important Questions

Most expected questions

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FAQ

1. Are the Chapter 1 notes available for free?

Yes. You can download the Chapter 1 study notes PDF for free and use them for revision and exam preparation.

Yes. All study materials are prepared according to the latest CBSE Class 10 Mathematics (2026–27) syllabus and are updated whenever required.

Yes. Step-by-step NCERT textbook solutions are available to help you understand every exercise and question.

Yes. Detailed NCERT Exemplar solutions are provided for additional practice and advanced problem-solving.

Yes. This chapter includes CBSE Previous Year Questions with solutions to help you understand the latest exam pattern.

Yes. Chapter-wise MCQs based on the latest CBSE exam pattern are available for quick revision and self-assessment.

Yes. Assertion & Reason questions and Case Study Questions are included to help you prepare for competency-based assessments.

Yes. The complete Chapter 1 video lesson is embedded on this page, and you can also watch it on our YouTube channel.

Yes. A chapter-wise formula sheet is available for quick revision before tests and board exams.

Yes. A visual mind map is provided to help you quickly revise the important concepts of Chapter 1.

Yes. You can download the practice worksheet to improve your problem-solving skills and prepare for school and board examinations.

Simply click the “Next Chapter” button at the bottom of this page to continue your Class 10 Mathematics learning journey.

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