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Sūtra 14 of 16

Ekanyūnena Pūrveṇa

By one less than the previous one

Multiplying by a number consisting of all 9s.

When to use

Multiplications like 67 × 99, 543 × 999.

How it works

Left part: subtract 1 from the original number. Right part: complement of original (digits subtracted from 9, last from 10). Concatenate.

Memory formula

Multiply by 99…9: left = number − 1; right = base complement of the number.

Worked examples

Problem 1
67 × 99
0/3
    Problem 2
    543 × 999
    0/3

      Try it yourself

      Try to solve, then reveal the steps one at a time.

      easy
      Compute 56 × 99
      medium
      Compute 783 × 999

      Modern applications

      Where this ancient technique still lives in today's world.

      Coding

      Multiplying by 9-strings

      Multiplying by 999…9 is a one-instruction trick (shift + subtract) used in optimised low-level numeric kernels.

      Code in your favourite language

      Multiply by 9, 99, 999 by subtracting 1 then taking the complement.

      Python
      def by_nines(n: int, nines: int) -> int:
    base = 10 ** nines
    return (n - 1) * base + (base - n)

print(by_nines(56, 2))  # 5544

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