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:
 
YCIND_260109_7871_Symbol (2).svg
Regrouping the number of 111333.png and YCIND_260123_7927_10.png we get,
 
\(15\) YCIND_260123_7927_10.png and \(15\) 111333.png
 
From the above table we get,
 
YCIND_260123_7927_10.png \(= 10\)
 
111333.png \( = 1\)
 
From the table we get, 
 
\(10\) YCIND_260123_7927_10.png \(=\)  YCIND_260123_7927_10^2.png
 
\(10\) 111333.png \(=\) YCIND_260123_7927_10.png
 
Thus we get,
 
 
\(15\) YCIND_260123_7927_10.png \(= (10 \)YCIND_260123_7927_10.png \(+\) \(5\) YCIND_260123_7927_10.png
 
\(=\)YCIND_260123_7927_10^2.pngYCIND_260123_7927_10.pngYCIND_260123_7927_10.pngYCIND_260123_7927_10.pngYCIND_260123_7927_10.pngYCIND_260123_7927_10.png  ------ (1)
 
\(= (10 + 5 ) \times 10\)
 
\( = (10 \times 10\) + (5 \times 10)\)
 
\(15\) 111333.png \(= (10 \)111333.png \(+\) \(5\) 111333.png
 
\(=\) YCIND_260123_7927_10.png111333.png111333.png111333.png111333.png111333.png ------ (2)
 
Thus the sum of (1) and (2)
 
\(=\) YCIND_260123_7927_10^2.pngYCIND_260123_7927_10.pngYCIND_260123_7927_10.pngYCIND_260123_7927_10.pngYCIND_260123_7927_10.png
        YCIND_260123_7927_10.pngYCIND_260123_7927_10.png111333.png111333.png111333.png111333.png111333.png
 
Question 2:
 
Find the product of the following:
 
product of base n.jpg
 
Solution:
 
From the table we get,
 
YCIND_260123_7927_10.png \(=10\)
 
product of base n.jpg \(=10 \times 10\)
 
\(=10^{2}\)
 
\(=\)YCIND_260123_7927_10^2.png
 
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:
 
\( 640 = (10) \times 60 + 40\)
 
\(=\) \(10 \times\) YCIND_260123_7927_60.png \(+ 4 \times\) 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