Cube Of Three Digit Number Less Than The Base


Cube With Yavadunam Method I - Concepts
Class - 7th IMO Subjects
 
 
Concept Explanation
 

Cube Of Three Digit Number Less Than The Base

Cube of a Three Digit Number Less Than The Base Using Yavadunam Method

This method is used to find the cube of a three digit number less than the base. It is a very efficient way of finding Cube. It saves a lot of time in competitive exam where each second counts and doing these type of calculations in normal ways consumes lot of our precious time.

Finding Cube of 996

Step 1 : Find the deficit in the number as compared to the base. For 996 the nearest base is 1000 so the deficit is 4 or we can say surplus will be -4

We will double the surplus and add it to the number

Result 1 = -4 X 2 + 996 = -8 + 996 = 988

Step 2: The surplus in the Result 1 that is 988 when the base is 1000 is -12. We will multiply the surplus with the earlier surplus i.e. -4 Result 2= -12 X -4 = 48

Step 3: Find the Cube of the number that was surplus in step1. Cube of -4 is -64

Result 3 = -64

Since the total zeros in the base are three, so three digits will we be prefixed in the answer at each step.

Step 4: As the Result 3 is negative We will borrow 1 from result 2 add 1000 to the result 3, Then the three digits will be prefixed in the answer and the remaining are the carry.

Resultant Number= 1000 -64 = 936

Result 2 = 48-1 = 47

Answer = 936

Carry is 0

Step 5: The carry is added to Result 2 Then the three digits will be prefixed in the answer and the remaining are the carry. If the digits are less than three then zeros are prefixed.

Resultant Number = 047

Answer 047936

Carry is 0

Step 6: The Carry is added to the Result 1. The Resultant Number is Leftmost Block of the Answer

Resultant Number = 988 + 0 = 988

Answer : 988047936

 

 
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