Estimation tricks for mental math

Most real-world mental math does not need an exact answer. It needs a close one, fast, and a sense of whether a number is wrong. These are the techniques that get you within a few percent in seconds.

Round one number up and the other down

When multiplying, rounding both numbers the same way makes the error grow. Round them in opposite directions and the errors partly cancel.

For division, do the opposite: round both numbers the same way. 487 ÷ 52 ≈ 500 ÷ 50 = 10 (exact: about 9.37).

Count the zeros separately

With big numbers, handle the leading digits and the powers of ten as two separate problems. 40,000 × 3,000 is 4 × 3 = 12, with 4 + 3 = 7 zeros: 120,000,000. Writing large numbers as a digit times a power of ten (4 × 10⁴) makes this automatic.

The rule of 72

To find how long something growing at r% a year takes to double, divide 72 by r. At 6% it takes about 12 years; at 9%, about 8. It is accurate to within a few percent for rates between about 2% and 15%.

Percentages as fractions

Swap awkward percentages for nearby fractions: 33% ≈ ⅓, 12.5% = ⅛, 16.7% ≈ ⅙. 17% of 240 is roughly ⅙ of 240 = 40 (exact: 40.8). More in percentages in your head.

Sanity-check every answer

• Order of magnitude: is the answer in the hundreds or the thousands? An estimate catches a misplaced zero immediately.
• Last digit: 37 × 43 must end in 1, because 7 × 3 = 21.
• Parity: an odd number times an odd number is odd.

Estimation is a core skill in quant and trading interviews, where a fast, close answer often beats a slow, exact one. See mental math for trading interviews.