Percentage errors are everywhere in everyday money. They compound into real losses — on tips, sale prices, taxes, and business pricing. Three common traps and how to avoid them.
Mistake 1: Stacking discounts like they add
"20% off storewide plus 20% extra at checkout!" sounds like 40% off. It isn't. The second 20% comes off the already-discounted price:
$100 → (20% off) → $80 → (20% off again) → $64. Total discount: 36%, not 40%. The store won.
Mistake 2: Confusing discount and markup
A $100 item marked 50% off sells for $50. Simple. But going back from $50 to $100 requires a 100% markup, not 50%. This asymmetry trips up small business owners constantly — they mark up 50% and wonder why their margin is only 33%.
Margin is profit ÷ selling price. Markup is profit ÷ cost. Same profit, different denominators, different percentages. A 100% markup produces a 50% margin.
Mistake 3: Reverse sales tax done wrong
You have a receipt total of $108 with 8% sales tax. What's the pre-tax price?
Wrong: $108 − 8% of $108 = $108 − $8.64 = $99.36.
Right: $108 / 1.08 = $100.
Why? The $8 tax was on the $100, not the $108. Subtracting 8% of $108 over-removes. Always divide by (1 + rate) to reverse a tax.
The meta-mistake
All three are variations of the same issue: percentages are ratios, and ratios depend on what you're dividing by. When in doubt, write out the math in dollars: you can't fool yourself with raw numbers the way you can with percents.
Three modes. Shareable URLs. Save your math instead of trusting your gut.