Real Numbers
Number System
Let us once recall the Types of Numbers that we know till now.
Natural Numbers :
The Counting numbers are called 'natural numbers' which are denoted by
N = {1,2,3,4,5,........}
Whole Numbers :
Zero and all the natural numbers are together called 'whole numbers'
which are denoted by W = {0,1,2,3,4,........}
Integers :
All the negative numbers, zero and all positive numbers are called
'Integers' denoted by Z = {-3,-2,-1,0,1,2,3,4}
Rational Numbers
Any number which can be expressed in the form p/q, where p&q are integers and
q = 0 are called 'rational numbers. Such numbers are denoted as Q = {5/3, 7/2,
8/5,} etc....
, Irrational Numbers :
Numbers which cannot be expressed in the form p/q are called 3 5 'irrational
numbers'. E.g: √2 , √3 , √5 , √11 , etc......
Real Numbers :
All the rational numbers as well as the irrational numbers are called 'real numbers'.
Prime Numbers :
Those numbers which have only two factors i.e. 1 and the number itself are called
'Prime Numbers'.E.g: 2,3,5,7,11, etc....
Composite Numbers :
Numbers having more than two factors i.e 1, the number itself and some other
number(s) are called 'Composite Numbers'. E.g: 4,6,8,9,10,12, etc....
*Note: 1 is neither prime number nor a composite number as it has only one factor.
Fundamental Theorem of Arithmetic
"Every composite number can be expressed (factorised) as a product of primes, and
this factorisation is unique, apart from the order in which the prime factors occur".
Example: Express 32760 as a product of primes.
2 32760
Solution: 32760 = 2 × 2 × 2 × 3 × 3 × 5 × 7 × 13 2 16380
2 8190
32760 = 2³ × 3² × 5 × 7 × 13
3 4095
3 1365
#Toh ye hamne ek composite number (32760) ko
5 455
prime numbers ke product ki form me express kar
7 91
diya hai jaisa ki theorem kehta hai...OK.
13 13
1
Number System
Let us once recall the Types of Numbers that we know till now.
Natural Numbers :
The Counting numbers are called 'natural numbers' which are denoted by
N = {1,2,3,4,5,........}
Whole Numbers :
Zero and all the natural numbers are together called 'whole numbers'
which are denoted by W = {0,1,2,3,4,........}
Integers :
All the negative numbers, zero and all positive numbers are called
'Integers' denoted by Z = {-3,-2,-1,0,1,2,3,4}
Rational Numbers
Any number which can be expressed in the form p/q, where p&q are integers and
q = 0 are called 'rational numbers. Such numbers are denoted as Q = {5/3, 7/2,
8/5,} etc....
, Irrational Numbers :
Numbers which cannot be expressed in the form p/q are called 3 5 'irrational
numbers'. E.g: √2 , √3 , √5 , √11 , etc......
Real Numbers :
All the rational numbers as well as the irrational numbers are called 'real numbers'.
Prime Numbers :
Those numbers which have only two factors i.e. 1 and the number itself are called
'Prime Numbers'.E.g: 2,3,5,7,11, etc....
Composite Numbers :
Numbers having more than two factors i.e 1, the number itself and some other
number(s) are called 'Composite Numbers'. E.g: 4,6,8,9,10,12, etc....
*Note: 1 is neither prime number nor a composite number as it has only one factor.
Fundamental Theorem of Arithmetic
"Every composite number can be expressed (factorised) as a product of primes, and
this factorisation is unique, apart from the order in which the prime factors occur".
Example: Express 32760 as a product of primes.
2 32760
Solution: 32760 = 2 × 2 × 2 × 3 × 3 × 5 × 7 × 13 2 16380
2 8190
32760 = 2³ × 3² × 5 × 7 × 13
3 4095
3 1365
#Toh ye hamne ek composite number (32760) ko
5 455
prime numbers ke product ki form me express kar
7 91
diya hai jaisa ki theorem kehta hai...OK.
13 13
1
