The sutra (formula) that empowers me to divide by numbers ending in 9 is again "Ekadhikena Purvena" meaning by one more than the previous one
The division can be done in two ways - by division and by multiplication .
I will take up by multiplication in this article. I will illustrate by taking two examples, 1/19 and 1/7 = 7/49
The numerator in 1/19 is 1. So, we start with 1.
Digit previous to 9 is 1 and one greater than 1 is 2. We will deal with multiplications by 2 only.
Multiply 1 by 2 to get 2
Now, we have 21.
Multiply 2 by 2 to get 4
Now, we have 421.
Multiply 4 by 2 to get 8
Now, we have 8421.
Multiply 8 by 2 to get 6 as base-number and 1 as carry over.
Now, we have 168421.
Multiply base-number 6 by 2 to get 2 as base-number and 1 as carry over. Add the previous carry over 1 to get 3 as base number.
Now, we have 1368421.
Carry on till you have a total of (19-1)/2 = 9 digits in place. And they would be 947368421. We call is Lower Half. To calculate the Upper Half, take 9's complement.
999999999 -947368421 ------------ 052631578 ------------
The result, therefore, is:
0.052631578947368421
Enjoy! Now the example of 1/7. It will contain a total of 7 - 1 = 6 digits that will recur.
1/7 = 7/49. The number previous to 9 is 4 and one next to 4 is 5.
First, write 7. Multiply by 5, yielding 5 as base-number and 3 as carry overy - 357. The full chain is as below:
7 => 357 => 2857 => 42857 => 142857Therefore,
1/7 = 0.142857
No comments:
Post a Comment