The % Trap: How Fractions, Decimals and Percentages Play Tricks on You

Next time you see a sale advertised as “20% off,” you might assume adding 20% back will undo the discount. Spoiler alert: it won’t. Fractions, decimals and percentages are simply different ways to describe parts of a whole, but when you mix them without converting properly, you can end up in for a rude surprise. Let’s explore why these three number formats sometimes play tricks on our intuition.

Where did this come from?

Fractions are ancient: Egyptians around 1800 BC used only unit fractions (like 1/2, 1/3) and combined them to describe any quantity. Decimal fractions didn’t appear until the late 16th century, when Belgian mathematician Simon Stevin published a pamphlet promoting a base-10 fractional system—think of it as an early pitch for our modern decimal point. Percentages, literally “per hundred,” trace back to Roman times but became widespread in medieval Europe as merchants and money-lenders calculated interest rates and taxes.

Where you'll see this in real life

1. Shopping discounts: two successive percentage changes (–20% then +20%) don’t cancel out, because the second change is on a smaller number. 2. Bank interest and fees: knowing whether rates are quoted as simple, compound, or annualised percentages can save you serious cash. 3. Cooking and recipes: swapping 0.25 of a cup (fraction) for 60 mL (decimal) works, but converting them wrong can ruin the bake. 4. Sports stats: a batter hitting .300 in baseball has a decimal batting average, which is really 30%—they’re all intertwined.

A common misconception

Many people assume “increase by 20% then decrease by 20%” brings you full circle. But imagine a $100 item: 20% off makes it $80. A 20% increase on $80 is only $16, bringing you to $96—not $100. The lesson? Always convert percentages into fractions or decimals (20% = 0.20) before doing your calculations, and keep track of what base you’re working from!