Vedic Maths - Calculating Complements

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Many of our friends are asking us to post detailed notes about finding Complements. This post is for them, who don't have the basic idea bout Complements. Happy Reading :).

What is Complement of a number ?

The Complement of a number is the difference between that number and the next higher power of 10. 3 is the complement of 7 (as next higher power of 7 is 10). 34 is the complement of 66 (as next higher power of 66 is 100). Still confused ? Let it be more simple.

• 10's complement - For any number less than 10, the number that should be added to make it 10.
• 100's complement - For any number less than 100, the number that should be added to make it 100.

In vedic maths we call this technique as "Nikhilam Navatah Charamam Dasatah". This means, All from 9 and last from 10.

Details : We have to get the complement (Nikhilam) for the entire number by using 10 for the digit in the units place and by using 9 for the remaining digits. Let us try to get the concepts before using this sutra.

• Suppose we purchase a list of items worth of Rs. 68/- in a provision store. If we give Rs. 100/-, how much balance we have to get ? The answer given instantaneously is Rs. 32/-. Thus 32 is the complement of 68.
• For finding the above complement, we subtracted 68 from 100. But there are other methods also which are simpler than the above method of subtraction.
• For Example, to find the complement of 68,
• Identify the digit in the units place of the given number 68. It is 8.
• Find out the difference between 8 and 10. The answer is 2.
• The digit on LHS of 8 in the given number is 6.
• Find out the difference between this 6 and 9. The answer is 3.
• Arrange the differences in an order. The answer is 32.
• This 32 is the complement of the given number 68.
• Examples :
• The complement of 43 = 57
• The complement of 286 = 714
• The complement of 80497 = 19503

About The Author                                             

Rupali Shete (M.Sc., M.Phil., Ph.D) is a gold medalist from Osmania University (Hyderabad), one of the working members of Rananujan Mathematics Academy and Institute of Scientific Research on Vedas (ISERVE), Currently working in University of Pune.

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