﻿ Class 9 NCERT Math Solution
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TOPICS
Introduction

Introduction of number systems

A set of values used to represent different quantities is known as Number system. Natural Numbers

A number N is called a natural number, whoose start from 1 to above. i.e. 1,2,3,4,.....n.

Whole Numbers

A number W is called a whole number, whoose start from 0 to above. i.e. 0,1,2,3,4,.....n.

Integer Numbers

A number Z is called an integer number, whoose consist of +ve and -ve numbers. i.e. -n...-3,-2,-1,0,1,2,3...n

Integer Numbers are mainly two types:-
1. Positive Integers i.e. 1,2,3,4....n
2. Negative Integers i.e. -1,-2,-3,-4....-n

Rational Numbers

A number r is called a rational number, if it can be written in the form pq, where p and q are integers and q≠0. i.e. 0.3796, 4.1333...,45 etc.

Irrational Numbers

A number s is called an irrational number, if it cannot be written in the form pq, where p and q are integers and q≠0. i.e. √5 and 4.10100100010000... etc.

Complex Numbers (Imaginary Numbers)

A number i is called a comlex number, if it consist of -ve integer numbers in square root. i.e. √-5,√-2 and √-1 etc.

Real Numbers

A number R is called a real number, if it consist of rational numbers, natural numbers, whole numbers, integer numbers but not accept of complex numbers(imaginary numbers). i.e. √5,1,2,-4,-2,0.45,1.222...,45 etc.

Different Types of Numbers

There are mainly 7 types of Numbers which are following below :-

Even Numbers

Numbers which are exactly divisible by 2 are called even numbers. i.e. 2,4,6,.... Sum of first n even numbers = n(n+1).

Odd Numbers

Numbers which are not exactly divisible by 2 are called odd numbers. i.e. 1,3,5,.... Sum of first n odd numbers = n²

Prime Numbers

Numbers which are divisible by one and itself only are called prime numbers. i.e. 2,3,5,7,11....etc.

Relative Prime Numbers

Two numbers are said to be relatively prime if they do not have any common factor other than 1. i.e. (2,5),(3,7),(11,15)....etc.

Twin Primes

Two prime numbers which differ by 2 are called twin primes. i.e. (3,5),(5,7),(7,9),(13,15)....etc.

Composite Numbers

Numbers which are not prime are called composite numbers. i.e. 4,6,9....etc.

Perfect Numbers

A number is said to be a perfect number, if the sum of all its factors excluding itself is equal to the number itself. i.e. 6,28,496,8128....etc. Factors of 6 are 1,2,3 and 6. Sum of factors excluding 6=1+2+3=6. So 6 is a perfect number.

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