Multiplying numbers near 100
AI-drafted · awaiting admin review
Nikhilaṁ Navataścaramaṁ Daśataḥ: all from 9 and the last from 10.
निखिलं नवतश्चरमं दशतः
Nikhilaṁ Navataścaramaṁ Daśataḥ
Meaning: All from 9 and the last from 10
Example: 97 × 96
- Base 100: 97 is 3 below and 96 is 4 below.
- Cross-subtract: 97 − 4 = 93 (or 96 − 3, the same).
- Multiply the deficits: 3 × 4 = 12, written as two digits.
Answer: 9312
Find how far each number is from the nearest base (10, 100, 1000). 'All from 9 and the last from 10' is a quick way to find that deficit: for 97, 9 − 9 = 0 and 10 − 7 = 3, so 03. The left part of the answer is either number minus the other's deficit. The right part is the product of the deficits, with as many digits as the base has zeros. Numbers above the base work the same way with surpluses: 104 × 107 → 104 + 7 = 111 and 4 × 7 = 28, so 11128.