The Decimal Number System

 
 
 

Decimal Number System (Base-10)
    This number system uses TEN different symbols to represent values. The set values used in decimal are  0 1 2 3 4 5 6 7 8 9 with 0 having the least value and nine having the greatest value. The digit or column on the left has the greatest value, whilst the digit on the right has the least value. When doing a calculation, if the highest digit (9) is exceeded, a carry occurs which is transferred to the next column (to the left).
Example of addition and exceeding the base set range
8 + 4  becomes the steps....
                                8
                                9    +1
                               10   +2       Note A
                               11   +3
                               12   +4
Note A: When 9 is exceeded, we go back to the beginning of the set (0), and carry a value of 1 over to the next column on the left.

Another example of addition and exceeding the base set range
398 + 4  becomes the steps.....
                           398
                           399   +1
                           400   +2     Note B
                           401   +3
                           402   +4
Note B: When 9 is exceeded, we go back to the beginning of the set (0), and carry a value of 1 over to the next column on the left. Thus the middle column (9) has 1 added to it, the next value in the set is 0, and we carry 1 (because the set was exceeded) to the next left column. Adding the carry value of 1 to 1 in the left most column gives.

Positional Values [Units, Tens, Hundreds, Thousands etc Columns]
   We probably got taught at school about positional values, in that columns represent powers of 10. This is expressed to us as columns of ones (0 - 9), tens (groups of 10), hundreds (groups of 100) and so on.

243 = (2 groups of 100) + (4 groups of 10) + (3 groups of 1)
      = (100 + 100) + (10 + 10 + 10 + 10) + (1 + 1 + 1)
      = (200) + (40) + (3)
      = 243
Each column move to the left is 10 times the previous value.
 

   
                   
 

 

 
                   
 

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