Basic Math Class (Number Part-I)

1.  NUMBERS

    

IMPORTANT FACTS AND FORMULAE

I. Numeral

       In Hindu & Arabic system, we use ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 called digits to represent any number.

        A group of digits, denoting a number is called a numeral.

       We represent a number, say 689745132 as shown below :

Ten Crores (108)	Crores (107)	Ten Lacs (Millions) (106)	Lacs (105)	Ten Thousands (104)	Thousands (103)	Hundreds (102)	Tens (101)	Units (100)
6	8	9	7	4	5	1	3	2

      We read it as : 'Sixty-eight crores, ninety-seven lacs, forty-five thousand, one hundred and thirty-two'.

 II. Place Value or Local Value of a Digit in a Numeral

In the above numeral :

Place value of 2 is (2 x 1) = 2; Place value of 3 is (3 x 10) = 30;

Place value of 1 is (1 x 100) = 100 and so on.

Place value of 6 is 6 x 10⁸ = 600000000       

 

 III.Face Value

   The face value of a digit in a numeral is the value of the digit itself at  whatever place it may be.
   In the above numeral, the face value of 2 is 2; the face value of 3 is 3 and so on.

IV.TYPES OF NUMBERS

1. .Natural Numbers: 

          Counting numbers 1, 2, 3, 4, 5,..... are called natural numbers.

2.Whole Numbers: 
  
           All counting numbers together with zero form the set of whole numbers. Thus,

  
                  (i) 0 is the only whole number which is not a natural number.

                 (ii) Every natural number is a whole number.

3. Integers: 

         All natural numbers, 0 and negatives of counting numbers i.e., {…, -3,-2,-1, 0,    1, 2, 3,…..} together form the set of integers.

 (i) Positive Integers : {1, 2, 3, 4, …..} is the set of all positive integers.

(ii) Negative Integers : {- 1, - 2, - 3,…..} is the set of all negative integers. 
(iii) Non-Positive and Non-Negative Integers : 0 is neither positive nor negative. So, {0, 1, 2, 3,….} represents the set of non-negative integers, while {0, -1,-2,-3..} represents the set of non-positive integers.

4.  Even Numbers:

               A number divisible by 2 is called an even number, e.g., 2, 4, 6, 8, 10, etc.

5.  Odd Numbers: 

            A number not divisible by 2 is called an odd number. e.g., 1, 3, 5, 7, 9, 11, etc.

6.  Prime Numbers: 

            A number greater than 1 is called a prime number, if it has exactly two factors, namely 1 and the number itself. Prime numbers upto 100 are : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47,  53, 59, 61, 67, 71, 73, 79, 83, 89, 97. Prime numbers Greater than 100 : Let p be a given number greater than 100. To find out whether it is prime or not, we use the following method :

         Find a whole number nearly greater than the square root of p. Let k > *jp. Test whether p is divisible by any prime number less than k. If yes, then p is not prime. Otherwise, p is prime. e.g,,We have to find whether 191 is a prime number or not. Now, 14 > 191. Prime numbers less than 14 are 2, 3, 5, 7, 11, 13. 191 is not divisible by any of them. So, 191 is a prime number.

7.Composite Numbers: 

Numbers greater than 1 which are not prime, are known as composite numbers, e.g., 4, 6, 8, 9, 10, 12.

          Note :    (i) 1 is neither prime nor composite.

           (ii) 2 is the only even number which is prime.

          (iii) There are 25 prime numbers between 1 and 100.

8.  Co-primes : 
        Two numbers a and b are said to be co-primes, if their H.C.F. is 1. e.g., (2, 3), (4, 5), (7, 9), (8, 11), etc. are co-primes.

To be Continued........