Numbers Near Base
The Nikhilam Sutra for numbers near 10, 100, 1000.
Core Concepts
The Nikhilam Sutra (All from 9 and the Last from 10) is incredibly powerful for multiplying numbers that are close to a "Base" like 10, 100, or 1000. It turns difficult multiplication into simple addition and subtraction!
The Method
1. Find the Deviation: How far is each number from the Base? (e.g., 104 is +4 from 100).
2. Cross-Add: Add one number to the other's deviation. This gives the first part of the answer.
3. Multiply Deviations: Multiply the two deviations together. This gives the second part.
Solved Examples
Example 1: Numbers Above Base 100
Question: Solve 103 × 104.
• Base: 100.
• Deviations: +3 and +4.
• Part 1 (Cross-Add): 103 + 4 = 107.
• Part 2 (Multiply): 3 × 4 = 12.
• Answer: 10712.
Example 2: Numbers Below Base 100
Question: Solve 98 × 97.
• Base: 100.
• Deviations: -2 and -3 (since they are less than 100).
• Part 1 (Cross-Subtract): 98 - 3 = 95.
• Part 2 (Multiply): -2 × -3 = 06. (Must be 2 digits for Base 100).
• Answer: 9506.
Example 3: Base 1000
Question: Solve 1005 × 1006.
• Base: 1000.
• Deviations: +5 and +6.
• Part 1: 1005 + 6 = 1011.
• Part 2: 5 × 6 = 030. (Must be 3 digits for Base 1000).
• Answer: 1011030.
Example 4: One Above, One Below
Question: Solve 104 × 98.
• Deviations: +4 and -2.
• Part 1: 104 - 2 = 102. (This is 10200).
• Part 2: 4 × -2 = -8.
• Subtract: 10200 - 8 = 10192.
