### 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 :

### 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.

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