Students often fear multiplication of numbers, which involve lot of 9’s in them. However the truth is exactly the opposite. The higher the number of 9’s in the question, the easier it is to calculate the correct answer.

There can be three cases with multiplication with series of 9’s

Here we are discussing Case 1 only and leaving the rest two cases for the readers to explore.

Question: Multiply 764 by 999

Question: Multiply 2345123 by 9999999

Subtract 1 from 2345123 to get 2345122 as left part of answer. Now subtract individual digits of 2345122 from 9 and write answer as 7654877. This becomes right part of answer. The final answer is 23451227654877

Use of Yavadunam Sutra for Finding square of a number near 100

Sutra Yavadunam function over a base value. The bases may be 10 , multiples of 10 or 100 , multiples of 100 or 1000 , multiples of 1000 etc. Here we limit ourselves to base 100 only.

The sutra says whatever be the difference of the number from the base add (if the number is more than the base) or subtract (if the number is less than the base) that much to the number and on the right hand side set the square of the difference. This gives us the final answer. Remember that the number of digits on right hand side is equal to the number of zeros in base.

Since 108 is 8 more than 100 therefore we have added 8 here as per the sutra and on the right hand side we set square of 8.

Since 98 is 2 less than 100 therefore we have subtracted 2 here as per the sutra and on the right hand side we set square of 2. See that we set 4 as 04 as the right hand side of the answer should have number of digits equal to the number of zeroes in the base.