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Squaring Near a Base

Square numbers close to 100 or 1000 in your head

The Rule

  1. 1Works when the number is close to a power of 10 — like 100 or 1000.
  2. 2Find the deviation d: how far the number is above or below the base (negative if below).
  3. 3Left part = the number plus d (this equals 2×number − base).
  4. 4Right part = d² (always positive), with as many digits as the base has zeros.
  5. 5If the right part has too many digits, carry the extra into the left part.