How to Multiplication of Three Digit Numbers Lesser than the Base

In the previous chapter, we used Nikhilam technique to multiply two digit numbers.

We will use the same technique in this chapter to multiply  3 digit numbers near 1000.

                     ( Using a base of 1000) 

( Both numbers are lower than the Base ) 

Multiplication : – 994 by 896

Step-1: Take the nearest power of 10, to these numbers.

Powers of 10 are 10,100,1000,10000… Thus nearest power of 10 to the numbers 994 and 896 is 1000. So we take 1000 as our base.

Step – 2 : Write the numbers one below the other.

Step – 3 : Subtract each of them from the base 1000. Write down the answer obtained as difference on the right side with a (- ) sign to show that the numbers are less than 1000.

Step – 4 : The product will have two parts: One on the left side and the other on the right. 

 Draw a slant line ( slash ) (/) to demarcate the two pats. multiply difference. The product is the Right Hand Side part of the answer.

Step – 5: The Left Hand Side of the answer can be obtained by crosswise addition, i.e. given number and the difference.

                  OR 

Answer : 890624

Multiplication : –  998 ×994 

Note : If Right Hand Side contains less Number of digits then the number of zeroes in base number, ( i.e.1000) then, the remaining digits are filled with Zero or Zeroes on the left side of the Right Hand Side number shown above.

Example – 3 : 877×986

Answer : 864722

Note – : If the number of digits are more then the number of zeroes in the base number expect the unit digit, the excess digit from the left side  ( here it is 1) is to be added to Left Hand Side of the answer as shown above.