Percentages in real life
Percentages aren't just a school topic. They show up everywhere outside the classroom, often when something is being compared or summarised in one number.
Shop discounts
The most common place to spot a percent: the sales rail.
−30 % on this jacket.
That means the price will go down by 30 %. If the jacket was £80, you save 30 % of 80 = £24, so it now costs £56.
A few discount tricks:
- "Half price" = 50 % off.
- "Buy one, get one free" = each item is effectively 50 % off (you get two for the price of one).
- "3 for 2" = three items for the price of two = each is effectively 33 % off (one third off).
School marks
Many tests are scored out of 100, which is why marks already look like percentages. If you scored 84 out of 100, you got 84 %.
If the test isn't out of 100, you turn it into a percent by writing the fraction and converting:
A 25-question quiz: you got 20 right.
Score = 20/25 = 80/100 = 80 %.
Battery and storage
Your phone screen says 27 % battery. That means 27 out of every 100 "units" of charge remain. When it hits 0 %, the battery is empty. When it's 100 %, the battery is completely full.
Same idea with disk space: "45 % full" means 45 out of every 100 units of storage are used.
Sports statistics
In football: "the team had 62 % possession". This means: out of every 100 seconds of play, the team had the ball for 62 of them.
In basketball: a "75 % free-throw shooter" makes 75 out of every 100 attempts.
Survey results
70 % of the children in our class have a dog.
If there are 30 children, then 70 % of 30 = 21 children have a dog.
Notice the trap: a percentage on its own doesn't tell you the actual number. "70 %" of a class of 30 is 21 kids, but "70 %" of a school of 600 is 420 kids. You need both numbers to know the count.
What percent NOT to trust
Sometimes percentages are used to make a number look bigger or smaller than it is.
- "Sales are up 200 %!" — if the shop sold 1 thing yesterday and 3 things today, that's a 200 % increase, but it's still only 3 things. The percent hides the small base.
- "99 % of users love it" — if only 50 users were surveyed, "99 %" is 49 or 50 people. Look for the sample size.
A percent is useful only when you know what whole it's measured against.
A puzzle
A trainer says: "I sold 150 % more shoes this year than last year."
Last year they sold 200 shoes. How many this year?
- 100 % of 200 = 200 (last year's number).
- 150 % of 200 = 300 (the increase).
- This year = 200 + 300 = 500 shoes.
(Increasing by 150 % is not the same as increasing to 150 %. The first is "add 150 % more on top", the second is "the new total is 150 % of the old".)