Number System

Introduction

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

 

Crores 

 

 

   Ten        Lacs(Millions)

       

           Lacs  

   

     Ten   Thousand 

    

 

 Thousands 

  

 

 Hundreds

     

   

 Tens 

 

 Units 

  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".

Place Value or Local Value of a Digit in a Numeral:-  PLACE VALUE or LOCAL VALUE of a digit in a numeral is the value of the digit, depending on its place. We can relate place with 'place value'

For Example:- Let Number is 689745132

Place value of 2 is \((2 \times 1)\) = 2

Place value of 1 is \((1 \times 100)\) = 100

Place value of 6 is \(6 \times 10^{8}\) = 600000000.

Face Value:- FACE VALUE of the digit in numeral is the value of digit itself, irrespective of its place in numeral.

For Example:- Let Number is 689745132

The Face value of 2 is 2.

The Face value of 3 is 3

Types Of Numbers

Different Type of Numbers:- 

1. Natural Numbers

2. Whole Numbers

3. Integers

4. Even Numbers

5. Odd Numbers

6. Prime Numbers

7. Composite Numbers

Natural Numbers:- Counting numbers 1, 2, 3, 4, 5, are called Natural Numbers.

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

  1.  0 is the only whole number which is not a natural number.
  2.  Every natural number is a whole number.

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.

Positive Integers:- {1, 2, 3, 4, 5, .... } is the set of all positive integers.

Negative Integers:- {-1, -2, -3, -4, ......} is the set of all negative integers.

Non-Positive and Non-Negative Integers:- 0 is neither positive nor negative. So, {0, 1, 2, 3, 4, ...} represents the set of non-negative integers, while {0, -1, -2, -3, -4, .....} represents the set of non-positive integers.

Different Type of Numbers

Even Numbers:- A number divisible by 2 is called an even number. eg, 2, 4, 6, 8, 10 etc.,

Odd Numbers:- A number not divisible by 2 is called an odd number. eg, 1, 3, 5, 7, 9, 11, etc.,

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 up to 100 are:- 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.