Percentages

Your phone battery shows 80%, a shop window advertises 30% off, and a download bar is stuck at 99%: percentages are everywhere in daily life. They are so popular because they make shares comparable, whether you are talking about 12 euros or 12 million. Once you know what the symbol really means, you can do many percentage problems in your head.

Percent means per hundred

The word percent comes from Latin and means per hundred. So 25% is simply 25 out of 100, written as the fraction 25/100. Picture the whole as a bar of 100 equal boxes: 25% of it is exactly 25 boxes. That is why 100% is always the whole and 50% is always half, no matter what you start with.

Fraction, decimal, percent: three ways to write it

Percentages, fractions, and decimals are three languages for the same share: 50% = 1/2 = 0.5 and 25% = 1/4 = 0.25. The conversion always works the same way: from percent to decimal you divide by 100, and you multiply by 100 to go back. So 7% becomes 0.07, and 0.4 becomes 40%. Once you can read all three, you spot shares at a glance.

Finding the percentage of a number

How much is 20% of 350? Calculate with the decimal: 0.2 · 350 = 70. Even faster is the 10% route: one tenth of 350 is 35, so 20% is double that, namely 70. That is exactly how you crack discounts in everyday life: if a jacket costs 80 euros with 25% off, you save 20 euros and pay 60 euros. For an increase you work out the part in the very same way but add it instead of subtracting: 10% on top of 50 euros is 5 euros, so 55 euros.