Ekanyūnena Pūrveṇa — By one less than the previous one

एकन्यूनेन पूर्वेण — Ekanyunena Purvena

By one less than the previous one. Multiply by a string of 9s: subtract 1 from the multiplicand for the left part; find the complement of the multiplicand for the right part.

Why it works: n × (10^k − 1) = n × 10^k − n = (n−1) followed by complement(n, k). Because 10^k − n is the complement of n with respect to 10^k: writing n in k digits and subtracting from 10^k gives the right portion.

Speed advantage: 1 mental step vs 9+ for multiplying by 9, 99, 999, 9999.

Best for

• Multiplying by numbers that are all 9s

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Originally published at https://www.sutraflow.app/sutras/ekanyunena-purvena