Class 9th Number System

basic concepts and important results

1.    Natural Numbers (N) :
    Counting numbers are known as natural numbers. Thus 1, 2, 3, 4, …etc. are natural numbers.
    ˜   The first and the least natural number is 1 (one)    
    ˜   Consecutive natural nos. differ by 1 (one). 

2.    Whole numbers (w) :
    All natural numbers together with '0' form whole numbers. Thus 0, 1, 2, 3, 4, … etc. one are whole nos.
    ˜   The first and the least whole number is zero.        
    ˜   Consecutive whole number differe by one.

3.    Integers (I or Z) :
    All natural nos. 0 and negative of natural nos. form integers for example. ……–4, –3, –2, –1, 0, 1, 2, 3, 4, … etc.
    ˜   O is neither a negative nor a positive number. It is a neutral no.

4.    Prime numbers (P) :
    A natural number, which is greater than 1 and divisible by one and by itself only, is called a prime number. For eg : 2, 3, 5, 7, 11, ……
    ˜   The smallest prime number is 2                
    ˜   Except 2 ; all other prime nos. are odd.

5.    Composite number (C) :
    A natural number, which is greater than 1 and is not prime, is called a composite number. Thus 4, 6, 8, 9, 10, 12, 14, ……
    ˜   The smallest composite number is 4.            
    ˜   A composite number can be even or odd.
    ˜  It has atleast three distinct factor.

6.    Co-prime numbers :
    If two numbers do not have any factor (other than 1) common; the numbers are said to be co-prime
    Thus (i) 6 and 25 are coprime, no any common factor other than 1. (ii) 3 and 5 are co-prime, no any common factor other than 1.
    ˜  It is not necessary that any of the two co-prime numbers has to be prime also.
    ˜  All consecutive nos. are coprime. 

7.    Terminating decimals :
    The decimal expansion ends after a finite number of steps of division. Such decimal expansions are called terminating decimals
    For example : = 0.4,        = 4.125    and so on.

8.    Non-terminating decimals :
    The decimal expansions never come to an end. Such decimal expansions are called non-terminating
    For example = = 0.1818…, =0.3555……

9.    Rational Numbers (Q) :
    The numbers of the form , where p and q are integers and q ¹ 0, are known as rational numbers.
or
    A number is rational if and only if it
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