CBSE NOTES Class 10 Mathematics Chapter-1. Real Numbers Key Points and Introduction



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CBSE NOTES Class 10 Mathematics Chapter-1. Real Numbers Key Points and Introduction

CBSE Notes for Class 10 Mathematics – chapter 1. Real Numbers: Key Points and Introduction | Free PDF & Exam-Focused Study Material

Get CBSE Notes for Class 10 Mathematics Chapter 1. Real Numbers: Key Points and Introduction prepared by experts as per the latest NCERT syllabus and CBSE exam pattern. These concise and easy-to-understand notes cover important definitions, formulas, diagrams, and key concepts from the chapter to help students in quick revision and effective exam preparation. Whether you are studying for school tests, board exams, or competitive exams, these notes provide a reliable study resource. Designed in simple language with point-wise explanations, they save time and enhance learning efficiency. Download free PDF notes, explore solved examples, and strengthen your understanding of [Topic Name] for scoring high marks. Perfect for Class 10 students who want clear, structured, and exam-oriented notes for CBSE Mathematics.

 

CBSE Notes ⇒ Class 10th ⇒ Mathematics

1. Real Numbers

Key Points and Introduction


Numbers

There are two types of Numbers.                                                        

1. Real Numbers

2. Complex Numbers (Real numbers + Imaginary Numbers)

Real Numbers: The numbers which can be represented on the number line by a unique point are called real numbers. 

Examples: -1, -2, -3, -4 ....................... , and 1, 2, 3, 4, 5.........................  

Complex Numbers: Coplex numbers are the numbers which consist of both real and Imaginary numbers.

Examples: 2 + i√3, where 2 is real part and i√3 is imaginary part. 

 

Real Numbers

(A)  Rational Numbers: The numbers which can be express in the form of p/q, and q0 such a numbers are known as real numbers. 

(B)  Irrational Numbers: The numbers which are not rational numbers but these an be represented on a number line, such numbers are known as irrational numbers. 

 

Rational Numbers

(I)  Integers:

      (a) Whole numbers: These are the set of positive integers from 0. Which                  have not decimal and fractional part. Such numbers are known as                        whole numbers.

           Example: 0, 1, 2, 3, 4, 5, ........................... 

           (i)  Natural Numbers: Natural numbers counting begin from 1 to ∞                             (infinty). such numbers are called natural numbers. 

                Ex: 1, 2, 3, 4, 5 ....................................... ∞. 

          (ii) Zero: 0 

      (b) Negative integers: The numbers before 0 on number line is called as                 negative integers these are -1, -2, -3, -4 ............................. -∞. 

(II) Fractional Numbers: 

      (a) Proper fraction

      (b) Improper fraction

 

Natural numbers

(a) Odd Numbers: The numbers which can not be divided by 2 are called odd           numbers. 

      Example: 1, 3, 5, 7, 9, 11, 13, 15 ................................................. ∞. 

(b) Even Numbers: The numbers which can be divided by 2 are called even             numbers. 

      Example: 2, 4, 6, 8, 10, 12, 14, 16 ................................................ ∞. 

(c) Prime Numbers:

(d) Composite Numbers:

(e) Co-prime Numbers:

(f)  Perfect Numbers:


 

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