← All sutras
All from 9 and the last from 10
Nikhilam Navatashcaramam Dashatah
The sutra name literally means: to find the complement of a number from a power of 10, subtract all digits from 9, except the last digit which you subtract from 10. For example, the complement of 879 from 1000 is 121 (8→9−8=1, 7→9−7=2, 9→10−9=1). This complement rule is then used as a shortcut for multiplication of numbers near powers of 10.
How It Works
- 1.The complement rule: to find how far a number is from the nearest power of 10, subtract each digit from 9, except the last digit from 10. E.g. for 97: 9−9=0, 10−7=3 → deficiency is 03 (i.e. 3).
- 2.For multiplication: choose the nearest power of 10 as the base (e.g. 100 for numbers in the 90s).
- 3.Find the deficiency of each number using the complement rule.
- 4.Cross-subtract: subtract either deficiency from the other number. 97 − 4 = 93. This gives the left part.
- 5.Multiply the two deficiencies: 3 × 4 = 12. This gives the right part. Combine: 93|12 = 9312.
Examples
97 × 96
Step 1 / 5
Multiply 97 × 96. Choose the nearest power of 10 as the base.
Number 197
Number 296
Base100
Try It Yourself
98 × 97