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?)
Threefold means “multiply by three” in my experience, so that would match your first example.
$100 increased threefold is $300.
$300 is 300% of $100.
$300 is a 200% increase from $100.
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.
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.
Is a onefold increase the same as a twofold increase?
No.
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?
Care to elaborate?
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.
But 46/42 = 1.095, so that would be a 9.5% increase.
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.
twofold = doubled, tripled = threefold.
onefold = singled, which doesn’t mean much at all.
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.
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%.
No, its 50 percent 
So true.
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%.
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.