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Nikhilam or Base Multiplication

Nikhilam Multiplication

Base Multiplication, also called “Nikhilam” multiplication, is a very useful technique in finding the product of multiplicand near bases or powers of ten.

“Nikhilam” comes from “Nikhilam Navatashcaramam Dashatah” which means “All from 9 and the last from 10” which will be discussed in Session 1 of the Vedic Math Webinars, Series 2 on July 22, 2021.

“All from 9 and the Last from 10” is used to quickly determine a “number’s deficiency from the base” or  how far the number is from the next higher power of 10

Consider the first question 88,889 x 99,998. With the digits of the multiplicands consisting of 8s and 9s, it would be very difficult to find the product if the conventional method is used given the number of regroupings needed.

By using “Nikhilam”, we can immediately see that their deficiencies are 11,111 and 2 respectively from 100,000.

The product is composed of two parts:

  1. The first part is simply 88,889 – 2 (or 99,998 – 11,111) = 88887
  2. And the 2nd part is 2 x11,111 or 22,222.

So the final answer is 8,888,722,222.

For the second question, 997 x 1124, it is easy to see that the first multiplicand 997 has a deficiency of 3 from 1000 while the other has an excess of 124 over 1000.

The first part of product is simply 1124 – 3 (or 997 + 124) = 1121 (which is really 1,121,000) while the second part is  -3 x 124 =  – 372. The final answer is 1,121,000 – 372 or 1,120, 628.

In the 3rd question, 9 of the small squares can be used to form a bigger square which is 3 x 3.3 cm or 9.9 cm on one side with the area 9.9 – 0.1 | 0.1 x 0.1 = 98.01. four of these square is 4 x 98.01 or 392.04 square centimeters.

More examples of base multiplication, and also multiplication of numbers with different bases like 9988 x 96 or numbers near multiples of powers of ten like 289 x 298 will also be discussed in Session 3, Vedic Math Webinars Series 2 on July 25, 2021.

Those interested in attending the webinar series may inquire from “MATH-Inic Philippines” for details.   

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