Ekanyunena Purvena-"By one less than the previous one"

777 multiplied by 999 = 776,223

(776 is one less than multiplicand 777 and 223 is the compliment of 776 from 9)

120 35 79 multiplied by 999 99 99 = 120 35 78, 879 64 21

1234 5678 09 multiplied 9999 9999 99 = 1234 5678 08 8765 4321 91

The Ekanyunena sutra can be used to derive the following results:

• Kevalaih Saptakam Gunyaat, or in the case of seven the multiplicand should be 143
• Kalau Kshudasasaih, or in the case of 13 the multiplicand should be 077
• Kamse Kshaamadaaha-khalairmalaih, or in the case of 17 the multiplicand should be 05882353 (by the way, the literal meaning of this result is "In king Kamsa's reign famine, and unhygenic conditions prevailed." -- not immediately obvious what it had to do with Mathematics. These multiple meanings of these sutras were one of the reasons why some of the early translations of Vedas missed discourses on vedaangas.)

These are used to correctly identify first half of a recurring decimal number, and then applying Ekanyuna to arrive at the complete answer mechanically. Consider for example the following visual computations:

1/7  = 143x999/999999 = 142857/999999 = 0.142857

1/13 = 077x999/999999 = 076923/999999 = 0.076923

1/17 = 05882353x99999999/9999999999999999 = 0.05882352 94117647

Note that

7x142857 = 999999

13x076923 = 999999

17x05882352 94117647 = 9999999999999999

which says that if the last digit of the denominator is 7 or 3 then the last digit of the equivalent decimal fraction is 7 or 3 respectively.