# CBSE Notes for class 10 th

## 1. Real Numbers : Key Points and Introduction Mathematics class 10th:English Medium NCERT Book Solutions

## NCERT Books Subjects for class 10th Hindi Medium

# 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 q≠0 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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