Consider the following two problems:
(A) Square 2 has sides that are longer than those of square 1 by a factor of 1.1. Compare the areas of the squares.
(B) Square 2 has sides that are longer than those of square 1 by 10%. Compare the areas of the squares.
I find that many college students majoring in the sciences get A right, but for B they compute $0.10^2=0.01$.
What is going on here? Does K-12 education in the US not ever teach students to convert a fractional difference to a ratio? (In the lower grades, it seems like the word "ratio" is for some reason coupled to notation like "2:3," and some students never realize that this connects to fractions.) Does the symbol % just trigger a sequence of operations in the student's brain, distracting from the larger context? Obviously the people who get $0.01$ aren't thinking about whether their answer makes sense. A contributing issue may be that they get little experience with problems in which the answer is a ratio.