## Multiplication of 3 digit number lesser than base

Multiplication of three-digit numbers

In Vedic Maths, Multiplication of three numbers can be done by Nikhilam Sutra (Base Method)

Case 2:-  When both Numbers are lesser than Base (1000)

For Example :- 992 x 997
Step 1 –

Number Base Difference
992 (X1) 1000 (Y)  - 8  (Z1)
997 (X2) 1000 (Y)  - 3  (Z2)

Y= nearest power of 10 i.e. 10, 100, 1000, 10000.
Thus nearest power of 10 to the number 992 and 997 is 1000.

1 = X 1 – Y, Z 2 = X 2 – Y (here Y is greater than X Therefore Z will be negative)

Step 2 -

Part A Part B
992-3 (-8) x (-3)
989 24

Part A = (X1 + Z 2)
Part B = Z1 x Z2

Step 3 -

Part A Part B
989 24
989 024

Ans :- 989024

Rule 1:- No. of zeros in base is equal to no. of digits in part B.
Here no. of zeros in base is greater than no. of digits in part B so we added one zero before number in part B
Now Club Part A with Part B for Final Answer

Another Example of Three Digit Numbers lesser than Base

995 x 993
Step 1 –

Number Base Difference
995 (X1) 1000 (Y)  - 5  (Z1)
993 (X2) 1000 (Y)  - 7  (Z2)

Y= nearest power of 10 i.e 10, 100, 1000, 10000.
Thus nearest power of 10 to the number 995 and 993 is 100.
Z 1 = X 1 – Y, Z 2 = X 2 – Y (here Y is greater than X therefore Z will be negative)

Step 2 -

Part A Part B
995- 7 (-5) x (-7)
988 35

Part A = (X1 + Z 2)
Part B = Z1 x Z2

Step 3 -

Part A Part B
988 35
988 035

Ans :- 988035

Rule 1:- No. of zeros in base is equal to no. of digits in part B.
Here no. of zeros in base is greater than no. of digits in part B so we added one zero before number in Part B
Now Club Part A with Part B for Final Answer.

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