The Secret Bond Between Fractions, Decimals and Percentages

Ever been dazzled by a 25% off sign and then paused, wondering what that really means—1/4 or 0.25? Fractions, decimals and percentages look like three separate tools in your maths toolkit, but they’re all just different ways of describing parts of a whole. Get ready to uncover why they’re more alike than you think, a quick dip into their past, and how this trio plays starring roles in everyday life.

Where did this come from?

Fractions are ancient: the Egyptians carved them into stone around 4000 BC, mostly using special unit fractions like 1/2, 1/3 and so on. Decimals arrived much later—Simon Stevin, a Flemish engineer, published a decimal notation in 1585 to make calculations simpler, though it took a while to catch on. Percentages, from the Latin per centum ("by the hundred"), were popular in medieval Europe for taxation and trade. Merchants loved them because talking about ‘per 100’ made splitting profits or taxes straightforward.

Where you’ll see this in real life

1. Shopping discounts: A 20% markdown is the same as paying 80% of the price or multiplying by 0.8. 2. Bank interest: If your account earns 1.5% annually, that’s 0.015 times your balance or 15/100 in fraction form. 3. Test scores: Scoring 18 out of 20 on a quiz means 90%, which you can also write as 0.9 or 9/10. 4. Cooking and recipes: You might halve a 3/4 cup of flour by turning it into 0.75 cups and then into 0.375 cups—converting back and forth keeps your baking on point.

A common misconception

People often add percentages directly—like thinking a 20% discount followed by another 20% off equals 40% total savings. In reality, the second 20% applies to the already-reduced price, not the original. To get the correct combined effect, convert to decimals (0.8 × 0.8 = 0.64) and realise you’re paying 64% of the original price, so you saved 36% overall.