Advantage of Base - n system:
 
There are two advantages in Base -n system
 
i) Addition of base -n system
 
ii) Multiplication of base -n system
 
Examples:
 
Question 1:
Addition of ENS.jpg
 
Solution:
Table value of Egyptian number system:
 
Eg.jpg
Regrouping the number of 1.jpg and 10.jpg we get,
 
\(15\) 10.jpg and \(15\) 1.jpg
 
From the above table we get,
 
10.jpg \(= 10\)
 
1.jpg \( = 1\)
 
From the table we get, 
 
\(10\) 10.jpg \(=\)  10^2.jpg
 
\(10\) 1.jpg \(=\) 10.jpg
 
Thus we get,
 
 
\(15\) 10.jpg \(= (10 \)10.jpg \(+\) \(5\) 10.jpg
 
\(=\)10^2.jpg10.jpg10.jpg10.jpg10.jpg10.jpg  ------ (1)
 
\(= (10 + 5 ) \times 10\)
 
\( = (10 \times 10\) + (5 \times 10)\)
 
\(15\) 1.jpg \(= (10 \)1.jpg \(+\) \(5\) 1.jpg
 
\(=\) 10.jpg1.jpg1.jpg1.jpg1.jpg1.jpg ------ (2)
 
Thus the sum of (1) and (2)
 
\(=\) 10^2.jpg10.jpg10.jpg10.jpg10.jpg
        10.jpg10.jpg1.jpg1.jpg1.jpg1.jpg1.jpg
 
Question 2:
 
Find the product of the following:
 
product of base n.jpg
 
Solution:
 
From the table we get,
 
10.jpg \(=10\)
 
product of base n.jpg \(=10 \times 10\)
 
\(=10^{2}\)
 
\(=\)10^2.jpg
 
Place Value Representation:
 
The Mesopotamian Number System 
 
It is a \(\text{base - 60 system}\). It is also called as \(\text{sexagesimal system}\). 
 
It is influenced by \(\text{Babylonian number system}\) 
 
Example:
 
\(\text{1 hour = 60 minutes}\)
 
\(\text{1 minute = 60 seconds}\)
 
Symbols:
Mesopotamian Number system.png
 
Example:
 
\( 640 = (10) \times 60 + 40\)
 
\(=\) \(10 \times\) 60.jpg \(+ 4 \times\) 10.1.jpg
 
640.jpg
 
Mayan Number System 
 
Mayan Number System.png
 
Chinese Number System:
 
Chinese number system.png
 
The Hindu Number System:
 
Hindu Number System.png