In high school I was taught a baby version of dimensional analysis in which the quantity you're trying to compute is either directly or inversely proportional to each of the quantities you're given, and the only pitfall is that you might divide when you should multiply or vice versa. In such a case, you keep yourself on the right path by including units along with the numbers, and checking that your big product-quotient expression has the right units. (For instance, you don't multiply distance by velocity if you want an answer that has units of time. m meters times v meters-per-second has units of meters-squared-per-second, while m meters DIVIDED BY v meters-per-second has units of seconds.) The Wikipedia page https://en.wikipedia.org/wiki/Dimensional_analysis does a pretty good job of explaining this. Anyway, I recall from high school chemistry that there were some pretty complex problems involving reaction rates of different chemical species where the keeping-track-of-units trick was really helpful because the complexity of the problem overloaded my short-term memory. Can anyone think of a problem (maybe chemical, maybe not) where keeping track of units, and trying to get them to cancel out, is really helpful? Of course, this is not to deprecate the sense-making approach that determines whether a number should be put "up top" or "down below" by asking "If this number were larger, would my final answer get bigger or smaller?" (My February "Mathematical Enchantments" essay will be about dimensional analysis, and I want to discuss these sorts of "baby" applications before I get into deeper ones where the exponents aren't all +1 and -1.) Thanks, Jim Propp