Fractions in Disguise
Percentages greater than 100
Find out whether a percentage can be more than 100, and what that would mean.
So far every percentage has been 100 or less. Can a percentage be more than 100? What would that even mean?
Kishanlal has opened a garment shop and wants at least ₹5000 of sales a day. Follow his first few days against that target.
| Day | Sales | % of target | |
|---|---|---|---|
| 1 | ₹2000 | (2000/5000) × 100 = 40% | 60% short |
| 2 | ₹3500 | (3500/5000) × 100 = 70% | 30% short |
| 3 | ₹5000 | 100% | exactly the target |
| 4 | ₹6000 | 120% | 20% over |
Look at day 4: ₹6000 is a thousand rupees more than the target. 1000 is 20% of 5000, so 6000 is 100% + 20% = 120%. The formula agrees: (6000/5000) × 100 = (6/5) × 100 = 120%.
So a percentage above 100 simply means more than the whole you're comparing against. He achieved 120% of his target: 20% more than it. The FDP trio still works: 120% = 6/5 = 1.2. (And 210% of the target would be 100% + 100% + 10%: ₹5000 + ₹5000 + ₹500 = ₹10,500.)
Everyday language does the same thing in words. If he made ₹2500 you could say he reached half his target, or 50%, or 0.5 of it. If he made ₹10,000 you could say he doubled his target, or made 2 times it, or 200% of it.
And a farmer whose harvest rose from 260 kg to 650 kg has (650/260) × 100 = 250% of last year's: another way of saying 2.5 times as much.
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