# 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*(10^{1}) + 8*(10^{0})

= 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*(10^{2}) + 4*(10^{1}) + 5*(10^{0})

= 100+40+5

= (145)_{10}

#### Pictorial Explanation

## 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*(10^{2}) + 2*(10^{1}) + 5*(10^{0}) + 6*(10^{-1}) +7*(10^{-2})

= 100 + 20 + 5 + 0.6 + 0.07

= 125.67