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
Example:
Question 1:
Add the following Egyptian numerals:
Solution:
Table value of Egyptian number system:
Regrouping the number of 
and 
we get,
and we get,\(15\) and \(15\)
and \(15\) From the above table we get,
\(= 10\) \( = 1\)From the table we get,
\(10\) \(=\) 
\(=\) \(10\) \(=\)
\(=\) Thus we get,
\(15\) \(= 10 \) \(+\) \(5\)
\(= 10 \) \(+\) \(5\) \(=\) ------ (1)
------ (1)\(= (10 + 5 ) \times 10\)
\( = (10 \times 10) + (5 \times 10)\)
\(15\) \(=10 \) \(+\) \(5\)
\(=10 \) \(+\) \(5\) \(=\) ------ (2)
------ (2)Thus the sum of (1) and (2)
\(=\)
Question 2:
Find the product of the following:
Solution:
From the table we get,
\(=10\) \(=10 \times 10\)\(=10^{2}\)
\(=\)
Abacus that makes use of the Decimal system:
People once counted using stones, sticks, and marks on wood. Later, the abacus was developed as one of the earliest calculating devices for performing basic arithmetic operations like addition and subtraction. It also helps us understand the decimal (base-10) place value system.
The abacus helped people represent numbers using beads on rods.
Each rod on an abacus represents a place value.
Bottom line: Units\((1s)\)
Second line: Tens\((10s)\)
Third line: Hundreds \((100s)\)
Fourth line: Thousands \((1000s)\)
To keep the board neat, each counter above a line has a value of \(5\), and each counter on or belwo the line has a value of \(1\).
Important!
Shortcomings of Egyptian system:
- The Egyptian number system worked reasonably well for numbers up to a crore \((10^7)\), but beyond that, it bacame impracical because there was no simple way to extend it for very large numbers.
- It needed a new symbol for every higher power of \(10\). That is, if the numbers became larger, the system became harder to write and manage.
So, the next number system was developed to make writing numbers easier and calculations simpler.