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Something increases threefold means it's up 300%, or 200%?
I'm a tad uncertain on this. I've always thought that when (say) $100 increases threefold, that's equivalent to saying it increased to 3 x $100 = $300, which in percent terms would be +200%. But I've seen some people (nonnative English speakers, FWIW) using a shorthand of "threefold" = "300%", which of course would yield a dollar figure of $400, not $300. Which is correct? (Or is my math screwed up either way?)







I'd say the difference is if you say it "increased by x%" or "increased to x%".
If you say it increased by 200% you'd get threefold. If you say it increased to 300% (of its original value) you get threefold. That's my crazy nonnative English speaker rationale. 




What's really fun is when you're dealing with something already expressed in percent. The nominal efficiency is 42 percent, but we've increased it by 4 percent. Ummmm, what does that mean?







Think of "___fold" as the same as saying "multiplied by ___" where ___ is the number used in the "fold" word.
Onefold = multiplied by 1 Twofold = multiplied by 2 And so on. Where percentages are concerned, it's like this: "x% of" works the same way, so 100% of $100 is $100. If you're adding it to something  say, "give him an additional 100% of $100" then obviously you're giving "him" $200. If something is "up" 100% then it has doubled in value  it is "up" by an amount equalling its own value, just as "up 50%" means that something has increased by half its value, or $50 in these examples. If you have $300 where you started with $100, then you now have 200% more than you started with, because increasing $100 by 200% is $300. If something is running at 42% efficiency then increasing it by 4% means it's now running at 46% efficiency. 




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If your efficiency goes from 42 percent to 46 percent, then you have increased the efficiency by 4 points. 




I see it as (and Im sure EVERYONE else does) taking 42 and increasing it by 4. If there is a situation where you would need to know what an exact 4% increase of a number is, you had better damn well know you need that exact number.







If I start in Reno with $1000 and I finish with $2000, I say "I doubled my money." I increased it by 100% ( 1 times the original amount ) so that I now have 200% of what I started with.
If I start in Reno with $1000 and I finish with $3000, I say "I tripled my money." I increased it by 200% (2 times the original amount) so that I now have 300% of what I started with. If I start in Reno with $1000 and finish with nothing, I am in the real world. 




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Saying "efficiency has increased by 4%" would mean 42% to 46%. Saying "output has increased by 4%" would mean 42% to 43.7%. 




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"X has increased by 4%" means that the new value of X is 104% of the old value of X, regardless of what you substitute for X. Note that in this particular case, the mathematical relationship between output and efficiency does not alter things, either: if you increase output by 4%, you are increasing the numerator in the efficiency calculation by 4%, ergo your efficiency will also increase by 4%. 






An increase in output doesn't neccessarily mean an increase in efficiency, eg stepping harder on the gas pedal will increase an engine's output but not its efficiency.





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For example assume your putting 100W of power into a machine. If it's only 42% efficient then the machine's producing 42W of power. A 4% increase in efficiency is measured against the power put in so 4W. A 4% increase in output is measured againt the 42W and so 1.7W. Fair enough, I was assuming a constant input for purposes of the example. 




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Percent change in X = ( NewX  OldX ) / OldX * 100% This is true regardless of whether X is efficiency, power, or cheeseburgers. 




No, not everyone does. I see the distinction between percentage points and just percent most commonly in political and economic contexts, and sometimes scientific ones.







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If a machine goes from 42% efficient to 46% efficient then efficiency has increased by 4%. The power output has increased by 9.5%. 




This is irrelevant. Don't make me stay up late.






















I understand what your saying.
I know that going from 10% to 12% is a 20% increase. I'm saying that going from 10% efficiency to 12% efficiency is a 2% increase in "efficiency" even though the "efficiency %" has increased 20%. If you don't see that then we'll just have to agree to disagree. 




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Why do you feel efficiency should be treated differently from any other percentage quantity, such as interest rate, or tax rate, or percentage of the population that are smokers? Not that I regard Wikipedia as the final arbiter of truth, but why do you feel that Wikipedia is just plain wrong in this case? Last edited by Machine Elf; 11022009 at 11:08 AM. 




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Assuming anyone on the other end will automatically be Spock is a recipe for disaster. The system efficiency was increased 20 percent, resulting in a overall efficiency of 12 percent rather than the nominal efficieny of 10 percent. Or some such bloviations. 




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Threefold $100= $300 = $100 + 200%(of $100) = 300% of $100. 




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Until about a year ago I worked in performance testing of power plant. Precisely because of the potential for confusion highlighted in this thread, it is common to express differences in terms of heat rate (effectively, the inverse of efficiency). A 4% improvement in efficiency is ambiguous  a 4% improvement in heat rate is not. 






billfish678 said:
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Why talk about a percentage increase of a percentage value? Are you talking about the value increasing by a certain number, or changing by a percentage of the value it was at? Why risk someone misinterpreting? State the original value and the final value, and don't worry about how much "percentage change" that is. Because if you state percentage change, 99% of the time the person is just going to need to convert that to the final value anyway. Skip the confusion, state the result. "We were running at 42% efficiency, but we increased to 46%." 




Does anyone know if the California car registration was increased by Grey Davis by a factor of 3 or 4? The goofball news media around here reported it as both a 3x increase and a 300% increase. I can't decide which way they misinterpreted it.





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Absolutely. The party raising taxes from 30% to 33% will say they are raising by 3%; their opponents will say they are raising taxes by 10%





Ha! The other day on the radio here something was referred to as having been DECREASED by 300%  as in its 300% smaller than its original size





Forget the math, I would love to know what efficiency means when its a percentage? Is it capacity, output as a measure of input, output vs potential output or some other combination?





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Threefold = 3x by default. Not x+3x. Increased Threefold = tripled. Increased Twofold = doubled. 




Percentages are a minefield of ambiguities. This is because they are the ratio of a quanitity compared with some base line but in everyday speech that baseline is usually implied and seldom explicitly stated. Furthermore it is quite possible for that baseline to change even when describing the same situation. For example  prices rose by 20% but later dropped by 20%.
It is one of many situations where the common vernacular is not precise enough to describe a mathematical concept. With careful phrasing most ambiguities can be eliminated, but this is not how most people speak or write. It helps little that politicians, the media and advertisers exploit this ambiguity to present themselves in a better light. 






Is it time for me to introduce my idea of... ecents!
It's just like percents... except it's natural logarithms. We all love logs, right? Well, although basee logs may be less logical for large values (vs base2, ie "doublings," or base10, ie "orders of magnitude"), for small values they line up with percents. E.g., 1.02x increase is 2% or 2 e%. Things diverge a bit for larger values, tho, so 1.5x is 40e% and 3x is 110e% Advantages: 2x more and 2x less is 100% and 50% respectively, but it's the same value in ecents! If you increase something by 20e% then decrease is by 20e%, you get back the same value! And there's no confusion as experience by the OP: it wouldn't make sense for ecents. Even the 42%>46% problem is avoided! 42% efficiency is actually 0.42 (not 1.42, etc.), hence it is precisely 86e% 46% efficiency is 0.46, and so 77e% 46/42 is 1.095, and so is 9e% YES! Last edited by Alex_Dubinsky; 11052009 at 12:12 AM. 




Cardinal said:
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bengangmo said: Quote:





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For example, an electric motor may use 100W of electricity, and deliver 95W of shaft power, giving an efficiency of 95%. The remaining 5% is lost as heat to the environment. In some cases, you may need to further specify the energy input term as "energy input that you pay for", so as to exclude energy that is taken "free" from the environment. 






It's the
3x is multiply by 3. Increase to 3x is to multiply by 3, or increase to 300%. Increase by 3x is to multiply by 3, then add that to the original, or increase by 300%. Friggin' words. 