the information leaflets for medication are written here (Germany) in case numbers and not in percentages, following a "1 in X" scheme (1 in 100, 1 in 1000, 1 in 10000) which I think kind of makes sense for inclusiveness, on the other side I do think this way is almost as if providing values on a logarithmic scale, due to the X in "1 in X" being given in base-10 magnitudes.

I wonder if it would actually be more intuitive to use dice for comparison. Like 1/36 would be the probability to roll doubles of 6, 1/216 would be the probability to roll triples of 6, etc. Rolling 6 dices to 6 would be 1/46656 and 7 dices to 6 would be 1/279936, ...

At least my generation has played enough Yatzeeh to have a feel for dice-throwing :-)

I think the point of that article (and the larger point about math anxiety) is that many people do not realize that 20% "just means" 20 in 100. And it probably gets worse for percentages < 1%.

From my encounters with mathematically unskilled people: The usage of percentages is very confusing. As in in it is used in "1 in 100" but also there is this "6% increase" which is used for factors 1.06, and that the reciprocal calculation is not a "6% decrease" but a "5.6% decrease". Then on top come usages of yearly or monthly interest rates, etc.

In each context, the percentage needs to be handled and understood differently, which means that even though percentages are everywhere, the knowledge does not automatically "solidify" upon being exposed to percentages for these folks.