Sunday, October 23, 2011

The Remainders by the Last Digit (Shesanyankena Charamena)

The Remainders by the Last Digit or Shesanyankena Charamena is used to express a fraction as a decimal to all its decimal places.It is similar to Ekadhikina Purvena .

Example 1:


a) Express 1/7 as a decimal

1. Add 'zero' to the numerator which makes 1 as 10
2. If the numerator is less than the denominator, add another 'zero' , else proceed as follows ...
3. Divide : (10)/7 = 1 remainder 3
4. Adding zero to the remainder (since it is less than the denominator), we divide as (30)/7= 4 remainder 2
5. We continue taking the remainder the following the steps from the start as follows :

 (20) /7 = 2 remainder 6
 (60) /7 = 8 remainder 4
 (40) /7 = 5 remainder 5
 (50) /7 = 7 remainder 1

6. Now note that the remainder is '1' which is same as the numerator '1'.This means we would get the repetition of the answers again and again.So we will stop here.

7. Using the numbers(remainders) 3,2,6,4,5,1 got above , we multiply them with the denominator '7',

7 x 3 = 2 1
7 x 2 = 1 4
7 x 6 = 4 2
7 x 4 = 2 8
7 x 5 = 3 5
7 x 1 = 7

8. Now we take the red shaded numbers from the above steps as sequence ,142857 (which would be our final result)

Therefore, Result (1/7) = 0.142857142857
PS: Similarly we can find the answers for other fractions using the same procedure as the above illustrated one .




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