Decimal Number System

Humans express numbers in decimal format which is also called the base 10 number system.

Decimal numbers = {0,1,2,3,4,5,6,7,8,9}


In general, base N number system will consist of numbers from 0 to N-1.

Example

Base 2 number system has numbers from 0 to 1. i.e 0 to (2 - 1).

Base 8 number system has numbers from 0 to 7. i.e 0 to (8- 1).




Positional Decimal Numbers

To represent numbers above 9, we are using positional decimal numbers.

Example

(18)10 consist of two decimal numbers which are 1 and 8.

Here,

The position of 8 is 0.

The position of 1 is 1.

Position count starts from the right side of a number.



18

= 1*(101) + 8*(100)

= 1*10+8*1

= 10+8

= (18)10


Example

145

The position of 5 is 0.

The position of 4 is 1.

The position of 1 is 2.



(145)10

= 1*(102) + 4*(101) + 5*(100)

= 100+40+5

= (145)10


Pictorial Explanation

positional decimal number




Real Numbers

When it comes to the real numbers or numbers with fractional parts, the position after the dot(.) will be counted as -1, -2 and so on.

Example

(125.67)10

The position of 6 is -1.

The position of 7 is -2.

The position of 5 is 0.

The position of 2 is 1.

The position of 1 is 2.



125.67

= 1*(102) + 2*(101) + 5*(100) + 6*(10-1) +7*(10-2)

= 100 + 20 + 5 + 0.6 + 0.07

= 125.67


Pictorial Explanation

positional decimal number with fractional parts



Useful Resources

https://en.wikipedia.org/wiki/Decimal

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