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  #1  
Old 11-02-2009, 01:38 AM
Koxinga Koxinga is offline
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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 (non-native 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?)
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  #2  
Old 11-02-2009, 01:55 AM
friedo friedo is offline
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Threefold means "multiply by three" in my experience, so that would match your first example.
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  #3  
Old 11-02-2009, 02:34 AM
ColdPhoenix ColdPhoenix is offline
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$100 increased threefold is $300.
$300 is 300% of $100.
$300 is a 200% increase from $100.
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  #4  
Old 11-02-2009, 02:52 AM
Alex_Dubinsky Alex_Dubinsky is offline
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I hate percents. How could a 50% difference be the same as a 33%? 200% same as 66%. It's infuriating. And then there's 300% of vs 200% more.
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  #5  
Old 11-02-2009, 04:08 AM
blueninja blueninja is offline
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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 non-native English speaker rationale.
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  #6  
Old 11-02-2009, 05:13 AM
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Is a onefold increase the same as a twofold increase?

Last edited by Reply; 11-02-2009 at 05:13 AM..
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  #7  
Old 11-02-2009, 05:21 AM
ColdPhoenix ColdPhoenix is offline
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Originally Posted by Reply View Post
Is a onefold increase the same as a twofold increase?
No.
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  #8  
Old 11-02-2009, 05:57 AM
ZenBeam ZenBeam is offline
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Quote:
Originally Posted by Alex_Dubinsky View Post
I hate percents. How could a 50% difference be the same as a 33%? 200% same as 66%. It's infuriating. And then there's 300% of vs 200% more.
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?
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  #9  
Old 11-02-2009, 05:58 AM
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Originally Posted by ColdPhoenix View Post
No.
Care to elaborate?
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  #10  
Old 11-02-2009, 06:19 AM
Mindfield Mindfield is offline
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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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  #11  
Old 11-02-2009, 06:24 AM
Mogle Mogle is online now
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Originally Posted by Mindfield View Post
If something is running at 42% efficiency then increasing it by 4% means it's now running at 46% efficiency.
But 46/42 = 1.095, so that would be a 9.5% increase.
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  #12  
Old 11-02-2009, 06:55 AM
Machine Elf Machine Elf is offline
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Originally Posted by ZenBeam View Post
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?
Strictly speaking, it means your new efficiency is 42% * 104% = 43.68%.

If your efficiency goes from 42 percent to 46 percent, then you have increased the efficiency by 4 points.
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  #13  
Old 11-02-2009, 07:03 AM
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twofold = doubled, tripled = threefold.

onefold = singled, which doesn't mean much at all.
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  #14  
Old 11-02-2009, 07:15 AM
DaveBfd DaveBfd is offline
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Originally Posted by Joe Frickin Friday View Post
Strictly speaking, it means your new efficiency is 42% * 104% = 43.68%.

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.
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  #15  
Old 11-02-2009, 07:35 AM
Ronald C. Semone Ronald C. Semone is offline
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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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  #16  
Old 11-02-2009, 07:35 AM
ColdPhoenix ColdPhoenix is offline
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Quote:
Originally Posted by Joe Frickin Friday View Post
Strictly speaking, it means your new efficiency is 42% * 104% = 43.68%.

If your efficiency goes from 42 percent to 46 percent, then you have increased the efficiency by 4 points.
Depends on the way it's phrased.

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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  #17  
Old 11-02-2009, 07:57 AM
billfish678 billfish678 is offline
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Originally Posted by Reply View Post
Is a onefold increase the same as a twofold increase?
No, its 50 percent
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  #18  
Old 11-02-2009, 08:15 AM
Serenata67 Serenata67 is offline
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Originally Posted by Ronald C. Semone View Post
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.
So true.
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  #19  
Old 11-02-2009, 08:19 AM
Machine Elf Machine Elf is offline
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Originally Posted by ColdPhoenix View Post
Depends on the way it's phrased.

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

Saying "output has increased by 4%" would mean 42% to 43.7%.
Why are you treating these two parameters (efficiency and output) differently when used in the same expression?

"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%.
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  #20  
Old 11-02-2009, 08:20 AM
Mogle Mogle is online now
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Quote:
Originally Posted by ColdPhoenix View Post
Depends on the way it's phrased.

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

Saying "output has increased by 4%" would mean 42% to 43.7%.
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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  #21  
Old 11-02-2009, 08:31 AM
ColdPhoenix ColdPhoenix is offline
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Quote:
Originally Posted by Joe Frickin Friday View Post
Why are you treating these two parameters (efficiency and output) differently when used in the same expression?

"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%.
Because in the two expressions we're talking about percentages of different things.

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.

Quote:
Originally Posted by Mogle View Post
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.
Fair enough, I was assuming a constant input for purposes of the example.
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  #22  
Old 11-02-2009, 08:32 AM
ColdPhoenix ColdPhoenix is offline
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Quote:
Originally Posted by Joe Frickin Friday View Post
Why are you treating these two parameters (efficiency and output) differently when used in the same expression?

"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%.
I just reread what you said. The 42% in both cases is the efficiency, as in the original example.
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  #23  
Old 11-02-2009, 08:37 AM
Machine Elf Machine Elf is offline
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Originally Posted by ColdPhoenix View Post
A 4% increase in efficiency is measured against the power put in so 4W.
A 4% increase in efficiency is not measured against the power put in; it's measured against the old value of efficiency.

Percent change in X = ( NewX - OldX ) / OldX * 100%

This is true regardless of whether X is efficiency, power, or cheeseburgers.
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  #24  
Old 11-02-2009, 08:40 AM
Animastryfe Animastryfe is offline
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Originally Posted by DaveBfd View Post
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.
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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  #25  
Old 11-02-2009, 08:49 AM
ColdPhoenix ColdPhoenix is offline
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Quote:
Originally Posted by Joe Frickin Friday View Post
A 4% increase in efficiency is not measured against the power put in; it's measured against the old value of efficiency.

Percent change in X = ( NewX - OldX ) / OldX * 100%

This is true regardless of whether X is efficiency, power, or cheeseburgers.
Efficiency is already a percentage of the power put in.

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

The power output has increased by 9.5%.
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  #26  
Old 11-02-2009, 09:01 AM
Machine Elf Machine Elf is offline
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Originally Posted by ColdPhoenix View Post
Efficiency is already a percentage of the power put in.
This is irrelevant. Don't make me stay up late.
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  #27  
Old 11-02-2009, 09:17 AM
Machine Elf Machine Elf is offline
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http://en.wikipedia.org/wiki/Percentage_point
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  #28  
Old 11-02-2009, 09:46 AM
Machine Elf Machine Elf is offline
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http://www.mathsisfun.com/percentage-points.html
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  #29  
Old 11-02-2009, 09:47 AM
Machine Elf Machine Elf is offline
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http://mathforum.org/library/drmath/view/64433.html
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  #30  
Old 11-02-2009, 09:53 AM
ColdPhoenix ColdPhoenix is offline
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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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  #31  
Old 11-02-2009, 10:07 AM
Machine Elf Machine Elf is offline
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Originally Posted by ColdPhoenix View Post
I'm saying that going from 10% efficiency to 12% efficiency is a 2% increase in "efficiency" even though the "efficiency %" has increased 20%.
The ambiguity embodied in your usage is the kind of thing that crashes rockets; this is why every engineer I've ever worked with, for clarity's sake, sticks to the usage I've described.

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; 11-02-2009 at 10:08 AM..
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  #32  
Old 11-02-2009, 10:55 AM
billfish678 billfish678 is offline
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Quote:
Originally Posted by Joe Frickin Friday View Post
The ambiguity embodied in your usage is the kind of thing that crashes rockets; this is why every engineer I've ever worked with, for clarity's sake, sticks to the usage I've described.
IME the really good ones state it in such a way that there CAN BE NO misinterpretation.

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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  #33  
Old 11-02-2009, 12:18 PM
pan1 pan1 is offline
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Originally Posted by Koxinga View Post
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 (non-native 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?)
Actually both 200% and 300% = threefold - depending on how you apply the math.

Threefold $100= $300 = $100 + 200%(of $100) = 300% of $100.
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  #34  
Old 11-02-2009, 04:08 PM
hibernicus hibernicus is offline
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Quote:
Originally Posted by ColdPhoenix View Post
Efficiency is already a percentage of the power put in.

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

The power output has increased by 9.5%.
Not really. Depending on why the efficiency has increased, the power output could have stayed the same, or increased or decreased by some other amount.

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.
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  #35  
Old 11-02-2009, 04:31 PM
Irishman Irishman is offline
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billfish678 said:
Quote:
IME the really good ones state it in such a way that there CAN BE NO misinterpretation.
This. Percentages are already something that is not intuitive to most people. Add to that the ambiguity of the language, and you have a recipe for disaster.

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%."
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  #36  
Old 11-03-2009, 02:38 PM
Cardinal Cardinal is offline
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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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  #37  
Old 11-04-2009, 01:58 AM
BigT BigT is offline
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Originally Posted by Irishman View Post
billfish678 said:


This. Percentages are already something that is not intuitive to most people. Add to that the ambiguity of the language, and you have a recipe for disaster.

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%."
In advertising and politics, sometimes confusion is the point. In these cases, pick the choice that shows the presenter in the worst light.
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  #38  
Old 11-04-2009, 04:30 AM
Superhal Superhal is online now
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Quote:
Originally Posted by Koxinga View Post
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 (non-native 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?)
If something triples in size, it's now 200% bigger than it used to be.
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  #39  
Old 11-04-2009, 04:41 AM
Koxinga Koxinga is offline
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My question was more one of English usage than of math per se. I'm just wondering how "a threefold increase" is commonly understood.

Myself, I tell people it's up 20,000 basis points.
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  #40  
Old 11-04-2009, 04:42 AM
amarone amarone is online now
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Originally Posted by BigT View Post
In advertising and politics, sometimes confusion is the point. In these cases, pick the choice that shows the presenter in the worst light.
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%
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  #41  
Old 11-04-2009, 07:34 AM
bengangmo bengangmo is offline
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Originally Posted by blueninja View Post
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 non-native English speaker rationale.
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
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  #42  
Old 11-04-2009, 07:40 AM
bengangmo bengangmo is offline
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Originally Posted by ZenBeam View Post
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?
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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  #43  
Old 11-04-2009, 09:41 AM
pan1 pan1 is offline
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Originally Posted by Koxinga View Post
My question was more one of English usage than of math per se. I'm just wondering how "a threefold increase" is commonly understood.

Myself, I tell people it's up 20,000 basis points.
Assume multiplication if its not clearly stated.

Threefold = 3x by default. Not x+3x.

Increased Threefold = tripled.
Increased Twofold = doubled.
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  #44  
Old 11-04-2009, 10:03 PM
j_sum1 j_sum1 is offline
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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.
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  #45  
Old 11-04-2009, 11:08 PM
Alex_Dubinsky Alex_Dubinsky is offline
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Is it time for me to introduce my idea of... e-cents!

It's just like percents... except it's natural logarithms. We all love logs, right? Well, although base-e logs may be less logical for large values (vs base-2, ie "doublings," or base-10, 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 e-cents! 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 e-cents.



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; 11-04-2009 at 11:12 PM..
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  #46  
Old 11-04-2009, 11:53 PM
bengangmo bengangmo is offline
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Gah - I saw it in the papers today.

A four fold decrease in consumption....
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  #47  
Old 11-13-2009, 05:23 PM
Irishman Irishman is offline
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Cardinal said:
Quote:
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.
Does that mean an increase to 3x or by 3x? Because by 3x is a 300% increase.

bengangmo said:
Quote:
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?
Yes. I think it's case specific. Contextual to that particular term.
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  #48  
Old 11-14-2009, 07:23 AM
hibernicus hibernicus is offline
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Quote:
Originally Posted by bengangmo View Post
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?
When talking about energy conversion (such as in an engine, a motor, a boiler, a turbine or a pump), it's an expression of useful energy output divided by energy input.

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.
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  #49  
Old 11-14-2009, 07:35 PM
Alex_Dubinsky Alex_Dubinsky is offline
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Originally Posted by Irishman View Post
Does that mean an increase to 3x or by 3x? Because by 3x is a 300% increase.
I've never heard this. 3x is always a multiplication. That's why the fn x is there.
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  #50  
Old 11-18-2009, 04:50 PM
Irishman Irishman is offline
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It's the ambiguity flexibility of language over the strictness of mathematics.

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.
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