My students regularly show me how easy it is to calculate extremely precise results. Now, whether they should trust that precision is a rather different questio

My students regularly show me how easy it is to calculate extremely precise results. Now, whether they should trust that precision is a rather different question, and one that even the good ones struggle with for a while. (In other news, I wish that more people paid attention to uncertainty propagation. Or heck, even just some oversimplified heuristics for significant figures.)