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Technically, "percent" should mean "for every hundred". So, I would think that it's perfectly fine to say "150%". However, in common usage, people rarely say percentages greater than a hundred. Is there an official grammarical rule for this?

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What gives you the idea that people rarely use percentages > 100%? There's a common idiom of "giving it 110%", i.e. giving more effort than usual, or giving your maximum effort. And that's just one example. –  Mr. Shiny and New 安宇 Feb 2 '12 at 15:37
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Percentages over 100% can be used, but should be used with care as they can very easily be misleading. See news.bbc.co.uk/2/hi/uk_news/magazine/7568929.stm and webcache.googleusercontent.com/… –  Hugo Feb 2 '12 at 16:19
    
I disagree that this is rare in common usage. Do you have a source saying it is? Anecdotally, there are plenty of examples, including articles about facebook growth, Apple stock, methane levels –  Peter Recore Feb 2 '12 at 19:21
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5 Answers

This is not a question of grammar, but of usage. As you note, "percent" means "for every hundred," so there is nothing at all wrong with percent values greater than 100 when discussing proportions, e.g. profits increased by 120%. Like fractions, however, percent values are longer to express than multiples, so for values much greater than 100 you may hear them less frequently:

The satellite reentered the atmosphere at over 2300 percent the speed of sound

versus

The satellite reentered the atmosphere at over 23 times the speed of sound

Percents greater than 100% may also be unsuitable if we are discussing fractions of a whole. To quote The Simpsons:

Hypnotist: You will give one hundred and ten percent...

Team: That's impossible. No one can give more than one hundred percent. By definition that is the most anyone can give.

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If your salary is $100,000 and mine is $150,000, then I make $150 for every $100 you make. Therefore my salary is 150% of yours. I don't see anything controversial about that. Note however that it would also be correct to say that my salary is 50% higher than yours.

However, if you are using percentages to refer to a part of a whole, typically it does not make sense to refer to more than 100% of a whole (unless perhaps something akin to debt is possible).

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There is some ambiguity with percentages as well. Your salary is 50% higher than his, so is his 50% lower? But his is also 33% lower, so is yours also 33% higher? –  Jon Purdy Feb 2 '12 at 17:08
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There's no ambiguity at all...stating X is 50% higher than Y absolutely does NOT say that Y is 50% lower than X. It's only ambiguous if you do not understand math. –  Michael McGowan Feb 2 '12 at 17:21
    
Hah, just being deliberately obtuse. I hear this kind of thing misstated all the time, especially the failure to distinguish between percentages and percentage points. –  Jon Purdy Feb 2 '12 at 17:30
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"My mother was half Jewish, half English, half Spanish." "That's three halves." "Oh, she was a big woman." –  Sam Feb 2 '12 at 18:12
    
I have a brother who is 12 feet tall. Well, I have a half-brother who is 6 feet tall, and two halves make a whole, so it's the same thing. –  Jay Feb 3 '12 at 3:34
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This isn't a question of grammar but of mathematics. But before it gets closed as out of scope, I'll slip in an answer.

People often say that percentages greater than 100 make no sense because you can't have more than all of something. This is simply silly and mathematically ignorant. A percentage is just a ratio between two numbers. There are many situations where it is perfectly reasonable for the numerator of a fraction to be greater than the denominator.

A common, if trivial, example is when a coach says, "You all have to give 110%!" There's always someone who will reply, "That's nonsense. How can someone give more than 100%?" Most likely the coach doesn't mean this as a literal number, but even if he does: 100% of what? If the coach means that the players should give 110% of the maximum that they are capable of, than that would be impossible by definition. But if he means that they should work 110% as hard as they've ever worked before, that's quite plausible. If the best I've ever done is to tackle 10 of the opposing team's players and this game I tackle 11, then I have done 110% of what I did before. If he means they should work 110% as hard as they THINK they are capable of, that's not necessarily unreasonable. Etc.

Sure, if someone says, "110% of dentists prefer our toothpaste", that would clearly be impossible. But, "Sales of our toothpaste this year were 110% of what they were last year" is quite plausible. If last year we sold 100,000 packages and this year we sold 110,000, then sales are 110% of last year's.

Even some "percentages of the whole" are meaningful. Like I saw a news story a couple of years ago that said that in a certain city (and I forget the exact number here, but something like ...) 105% of registered voters cast ballots in the election. That is, the total number of votes counted was more than the total number of people registered to vote. Obviously there was some sort of fraud or at least error, people who weren't registered nevertheless voting or people voting twice or someone altering vote totals. But while such a result would not be possible if everyone followed the rules and there were no mistakes, those are two big IFs, and clearly it is mathematically possible for the vote count reported to election officials to total more than the number of legal votes.

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That depends on what you mean by "common usage". There is nothing wrong with percentages greater than a hundred as far as grammar is concerned. However, these percentages are indeed used rarely in "common" speech because not everyone can grasp the notion of 150%. That is, it is not universally understood that 150% is one and a half, although it is universally understood that 50% is half.

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I think anyone with rudimentary math education should be able to grasp that! –  Cerberus Feb 2 '12 at 15:34
    
I agree with Cerberus: everyone who knows what a percentage is knows that 150% is 1.5. –  Mr. Shiny and New 安宇 Feb 2 '12 at 15:36
    
@Cerberus: The fact of the matter is that not everyone has rudimentary math education :) –  Armen Ծիրունյան Feb 2 '12 at 15:37
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@Armen: Like the old saying goes, there are 3 types of people in the world: Those who can count, and those who can't. –  Jay Feb 2 '12 at 16:30
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To answer the question, yes and no. In everyday communication to pass on an idea about something greater, fuller than an overflowing pot you may say a percentage over 100%.

In places where the mathematical value is given attention or is likely to get attention it is not.

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