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Giving it 110% – an insight into the meaning of percentages

In TV interviews you often hear of people giving ‘110 percent’ or similar. Recently in a photography forum someone posted review details of a piece of equipment saying that it had ‘138% of the sRGB colourspace’. The device you are reading this on probably defaults to the sRGB colourspace, it is basically the range of colours and tones that can be represented within the colourspace. Unfortunately the person disagreed with my assertion that there was a numerical flaw in the review in just the same way as when someone says ‘110% effort’.

In darts the 3 dart maximum score each turn is 180. You cannot get more than 180 so anything more than 100% of 180 is not possible.

In a confectionary multi-pack of 4 bars you can eat 0%, 25%, 50%, 75% or 100% of the bars in the pack. You cannot eat more than 100% of the pack without getting another pack.

Both of the above are finite sets each with their own fixed cardinality so there is a maximum of 100%.

If I have two cameras and buy a new one I’ll have 150% of the number of cameras that I had. It is not a finite set, the cardinality can change, so percentages greater than 100% are possible.

In 2009 my income was about 1080% more than my income in 1983. Income is, in some situations, not a finite set so you can go above 100%.

Colour spaces are finite sets, you cannot have more than 100%. If you do then you have gone outside of the cardinality of set of the colour space so you are no longer in that colourspace.

Effort is also a finite set, you cannot actually go beyond what is maximally possible, you cannot go beyond 100% effort.

Strangely the person who thought it was ‘OK’ to have 138% of sRGB patronisingly said that they ‘know I can do the math to understand the 138%’ ( the person is American, hence ‘math’ ). I certainly can do the mathematics to know when you can and cannot go above 100% of something.

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