Estimation technique and sanity-checking

Intuition

Mental math in a case is not a test of whether you're a human calculator. It's a test of whether you stay calm and accurate while talking. The trick isn't speed, it's simplification. You turn ugly numbers into friendly ones, work with powers of ten, and lean on a few reflexes (10% of anything, doubling, halving) so the arithmetic never traps you mid-sentence.

Think of it like driving a manual car. The first time it's overwhelming; with practice the gear changes happen without thought, freeing your attention for the road, or in this case, the business logic.

Framework

• Round to clean numbers, then adjust. 19% → 20%, 412M → 400M. Note the rounding so you can correct later if it matters.
• Decompose percentages into 10%s and 1%s. 12% = 10% + 2%; 35% = 25% (a quarter) + 10%.
• Use scientific shorthand for big numbers. Track zeros as ×10⁶ (million) and ×10⁹ (billion) so you never miscount them.
• Sanity-check by reframing. Convert the final number to a per-unit, per-day, or per-person figure and ask if it's believable.

Worked Example

"What's 15% of $3.2 billion in revenue?" Round to $3.2B. 10% = $320M. 5% = half of that = $160M. So 15% ≈ $480M. Sanity check: just under half a billion out of $3.2B, feels right for a 15% slice. You said the whole thing out loud, made no slip, and never reached for a calculator.

Now a division under pressure: "Profit is $4.5B across 18M customers, what's profit per customer?" The weak move is wrestling 4, 500, 000, 000 ÷ 18, 000, 000 with all the zeros attached. The strong move strips them first: 4, 500 / 18 = 250, the millions cancel, so $250 per customer. Sanity check: $250 of profit per customer would be absurd for a grocer but normal for a bank, say which world you're in. Ten seconds, zero zeros lost.

In the room

Never go silent into the math. Announce the simplification first: "19% is close to 20%, so I'll round, noting we're slightly overstating." Then narrate in anchor-steps, not digits: "10% of 3.2 billion is 320 million; half that again is 160; so 15% is about 480 million." Speaking in tens and halves lets the interviewer ride along, they should never wonder where a number came from. If you slip, fix it out loud and cheaply: "Hold on, I dropped a zero; that's 300 million, not 30." Catching your own error is a point scored, not lost. Close every calculation with the reframe: "That's about $480 million, just under half a billion, plausible for a 15% slice." The interviewer is scoring composure under arithmetic: clean numbers, voiced logic, and self-correction without flinching.

Pitfalls

• Carrying too many digits and losing the thread mid-calculation.
• Miscounting zeros on millions vs billions, the classic order-of-magnitude blunder.
• Skipping the sanity check and confidently reporting a number that's 10× off.