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?
Assume multiplication if its not clearly stated.
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… 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!
Gah - I saw it in the papers today.
A four fold decrease in consumption…
Cardinal said:
Does that mean an increase to 3x or by 3x? Because by 3x is a 300% increase.
bengangmo said:
Yes. 
I think it’s case specific. Contextual to that particular term.
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.
I’ve never heard this. 3x is always a multiplication. That’s why the fn x is there.
It’s the [del]ambiguity[/del] 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.
This is more about communication than math.