Ekadhikena Purvena in Converting Fractions to Decimals

Calculate the recurring decimal of fractions like 1/19 whose denominators end with 9. Learn a vedic math fraction tips and tricks.

Ekadhikena Purvena in Converting Fractions to Decimals

Conditions:

In fraction,

1) denominator value 1's digit must be 9
2) denominator value must be prime number (19, 29, 39, 59,...)

Calculation Rules :

1) Find the number of digit answer from denominator

n = denominator value - 1

2) First we find the half of the number of digit answer

m = n / 2

3) Find x from denominator value

Remove 1's digit and remaining value (Ekadhikena Purvena) add by 1

4) Always start with 1

5) Now, multiply last find digit to x value, if result is carry occurs to carry the value to next multiplication. Its up to reach m number of digits

6) Next to find the complement of rule 5 results of m digit values.

7) Now write answer from digit in reverse order from rule 6 and rule 5 with decimal point. Its Answer of given fraction value.


Example: 1/19

Rule 1 : n = 19 - 1 = 18
Rule 2 : m = 18 / 2 = 9
Rule 3 : x = 1 (Ekadhikena Purvena - digit previous to 9) + 1 = 2
Rule 4 : = 1 (first digit)
Rule 5 : = 1, (first digit)
1 * 2 (x) = 2,
2 * 2 = 4,
4 * 2 = 8,
8 * 2 = 16 (carry 1) = 6,
6 * 2 = 12 + 1 = 13 (carry 1) = 3,
3 * 2 = 6 + 1 = 7,
7 * 2 = 14 (carry 1) = 4
4 * 2 = 8 + 1 = 9
(m number of digits find i.e., 9 digits)
Rule 6 : 1 2 4 8 6 3 7 4 9
Complement (minus from 9) of this result is,
8 7 5 1 3 6 2 5 0
Rule 7 : digit in reverse order
0.052631578947368421
Result :
1/19 = 0.052631578947368421

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