What the heck is this Number system?

What is Number System and why it is important?

In this post, we will discuss what is number system and what are the various types of numbers in number system.

What is Number System?

A number system is a collection of various symbols, known as digits.

Different types of Number System

1. Binary Number System

A binary number system has a base of 2. It means thatin the binary number system, all the numbers can be represented by using 0 and 1.

The 2 symbols are 0 and 1

2. Decimal Number System:-

The number system which we follow is called as Decimal Number System where the base is 10.The base 10 indicates that there are 10 different symbols that we use.

0,1,2,3,4,5,6,7,8,9

These symbols are called as digits.

When we write a number in decimal system, the number on the extreme left is the most significant and the on the extreme right is the least significant..

In the decimal number system, The numbers have their place value according to their placement.

E.g in Number 3456

Place value of 3 = 3000

Place value of 4=400

Place value of 5=50

Place value of 6 is 6

And 3456 can be written as a sum of these numbers

3456=3000+400+50+6

Classification of Number System

A decimal number system has only 10 digits but using these 9 numbers , we can create infinite numbers.

You can't really think of a largest number..As a kid I always used to think that what is the largest possible number..


But there isn't any such number, as you can always add 1 to it and get even larger number.

The numbers thus formed can be divided into various categories depending on their nature..

●Real Numbers:

As a kid we studied about the number line. The number line has all the positive (including 0) and negative numbers.

7.8,-6.9,0,46.5,7/3,3.14

All these numbers are real numbers and they are not imaginary..

●Irrational numbers:-

The term rational comes from the word ratio..

The irrational numbers are those which can't be represented as a ratio..

E.g π
We usually consider π=22/7 but that's not an accurate representation.

22/7=3.142857142857142857...........
But π=3.141592653589793..............

We can see that 22/7 is only accurate up to 3.14, after which it is not accurate.

π is a never ending number, so we can never represent it in a form of a fraction .


Other examples of irrational numbers are
√2, √3
These are also never ending numbers , which we can't represent in the form of a ratio.

●Whole numbers:-

Have you ever tried counting the number of stars in the sky?●Whole number(complete)
Or
Have you ever counted the number of people ahead you in a queue?

If the answer to any of these questions is yes, then you're already familiar about the whole numbers.

The answer to any of these questions could be like 5,8,10,20,35,56 etc
These are numbers that represent whole things without pieces.They include all the positive numbers without fractions..

Of course there wouldn't be 76.43 stars , or 65/3 persons ahead you...hope you understood the concept of whole numbers..

-6,-7.9,3.14,5.6,1/2 These are not whole numbers.0,1,2,3,4,5,6,7,8 These all are whole numbers.

●Rational Number:

 These are the numbers which can be represented in the form of m/n, where m and n are integers and n is not equal to 0. It could be recurring or non-recurring

2/3, 6/7, 3/4 ,-6.7,4.9,0.5,0.33

These are examples of rational numbers

-6.7 is a rational number since it can be written as -67/10

4.9 is a rational number, since it can be written as 49/10

0.5 is a rational number, since it can be written as 1/2

0.3333333.... can be written as 1/3

●Integers:-

INTEGERS ARE whole numbers (not a fractional number) that can be positive, negative, or zero.

Examples of integers are: -9, 231, 5, 8.3, 97, and 4.043.


Examples of numbers that are not integers are: -1.43, 9 3/4, 3.14, 0.08, and 5,123.1.

●Fractions: (m/n)

A fraction denotes a part or parts of a unit. It is majorly classified into following types-


◆Proper Fractions: In a proper fraction the numerator is always less than the denominator. Proper Fractions are always less than 1.
E.g 4/7, 8/10, 6/13

◆ Improper Fraction: In an improper fraction the numerator is more than the denominator. Improper Fractions are greater than 1.
E.g 8/3, 9/2, 78/23

◆ Mixed Fraction: A mixed fraction consists of two parts.
An integer part and a fractional part. 
5 4/9, 3 4/11

●Natural Numbers: 

It is the set of positive numbers.Types of Numbers –

The natural numbers are  the numbers which we first learned as a kid.

1,2,3,4,5,6,7,8,9,10,11,12

 Some mathematicians also include zero in the natural numbers, but most of them exclude zero.

Some other ways of classification

●Even Numbers: Set of numbers exactly divisible by 2.

e.g 2,4,6,56,42,238 etc

●Odd Numbers: Set of numbers not exactly divisible by 2.
e.g 1,3,5,7,9,57,49 etc

●Prime Numbers: Prime numbers are the numbers which have no factor other than 1 and itself.

●Composite Numbers: Composite numbers have factors other than 1 and itself.
E.g 320=2x2x2x2x2x2x5

so 320 is a composite number

This were the classification of the number system. If you liked the post, please share it and leave a comment below.It would really motivate me.

Cheers! :)