What is the Number system?
1. Numbers - In Hindu-Arabic System, there are 'ten' digits namely
0,1,2,3,4,5,6,7,8,9
a number is denoted by a group of digits, Known as a Numeral.
2. Face value and Place value (Local Value) of a digit in a numeral-
(a) Face value - The face value of a digit in a numeral is its own value , at whatever place it may be .
example- In the numeral 6872 , the face value of 2 to 2, the face value of 7 is 7.the face value of 8 is 8 and the face value of 6 is 6.
(b) Place value - In a given numeral -
Place value of ones digit = (ones digit ) x1
'' '' '' ten Digit= (Ten digit) x 10
'' '' '' hundred digit = (hundred digit) x 100 , and so on .
Note:- Place value of 0 in agiven numeral is 0. at whatever place it may be .
3. Various types of Numbers-
(a) Natural numbers - Counting numbers are called natural numbers .Thus 1,2,3,4 ..... are all Natural number
(b) Whole numbers - All counting numbers , together with 0 form a set of whole numbers .
so, 0, 1,2,3,4 ...... are all whole numbers .
(c) Integers - All counting numbers , 0 and negetives of counting numbers , from the set of integers . So ....-3 , -2 , -1, 0,1,2,3,... are all integers .
set of +ve integers = {1 , 2 , 3 ,.......}
'' '' -ve '' = {-1, -2 , -3 .......}
'' '' all non negetive integers ={0,1,2,3,4 ......}
4. Even Numbers- A counting Number divisible by 2 in called an even number .
Thus 0 , 2 , 4, 6 , 8 ......... are all even numbers .
5. Odd Numbers - A Counting number not - divisible by 2 is called an odd number ,
so , 1 , 3 , 5, 7 , 9 , 11 ..... are all odd number .
6.Prime Numbers- A counting number is called a prime number if it has exactly two factors . namely itself and 1 example - All prime numbers less than 100 are : 2 , 3, 5, 7, 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 71 , 73, 79 , 83 , 89 , 97 .
7. Composite Number - All counting numbers . which are not prime , are called composite numbers , a composite number has more than 2 factors .
8.Perfect Numbers- A number the sum of whose factors (expect the numbers itself ) , is equal to the numbers , is called a perfect number . ex-6, 28, 496 ,
The Factors of 6 are 1, 2, 3 and 6 and 1+2+3=6
'' '' '' 28 ,, 1, 2 , 4, 7, 14 and 28 . and 1+2+4+7+14=28
9. Co- Primes or relative primes - Two numbers whose H.C.F is 1 are called co-prime numbers .
ex- (2,3 ) , (8 , 9) are pairs of co-primes .
(10) Twin Primes - two prime numbers whose difference is 2 are called twin primes .
ex- (3,5) , (5,7) ,(11,13) are pair of twin primes .
(11) Rational Number -Numbers which can be expressed in the form p/q , where p and q are integers and q ≠0 are called rational number .
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