(Cross-posted to innumeracy)
I saw an advert for a printer today that used the slogan “Was kostet 141% mehr Format?” (a bit difficult to translate, since that use of “Format” is not idiomatic for me even in German, but literally “What does 141% more format cost?”).
I only saw it from afar (enough to see the slogan and two pictures of printers), but I presume they were referring to printers that could print on A3 rather than A4 paper.
As you may know, the “A” series of paper sizes (defined in ISO 216 and commonly used in Europe, for example) have side ratios of 1:√2, which means that if you put two sheets next to each other along their long sides, they’ll be the same as the next bigger size of paper. So successive sizes have twice the surface area, and each side is √2 longer than the preceding size.
So “141% more format” is doubly wrong: even though it’s nonsensical to me at face value (I suppose, in printing there might be a jargon use of “format” that I don’t know…), the most obvious interpretation to me is area: but an A3 sheet of paper doesn’t have 141% more area than an A4 sheet: it has twice the area, or 100% more.
And even if they refer to side length: A3 isn’t 141% longer on each side, it’s 41% longer. Alternatively, it’s 141% of the length, but the ad referred to “141% more”.
I’m guessing the confusion arose from the fact that photocopiers in Europe often have predefined zoom values of 141%, 100%, and 71%, where 141% is useful for enlarging A5 to A4 or A4 to A3 (and 71% for the reverse)—so some poor innumerate person took the “141%” number relating A3 to A4 and made a slogan talking about “141% more”.
Which makes as much sense as telling someone who got a 2% pay raise that they are now earning “102% more money than before”.