This isn't really a homework question. It's a question about a book I'm reading out of curiosity, but this seemed to be the most appropriate place to put it. Also, it's not exactly a physics problem, but I did come across this issue while reading a physics related book. I apologize if this is the wrong section to post this question. But my question is: How do you keep track of significant figures for functions in general? For example, how would I know how many significant figures to keep in Sin(3.52)? Would I automatically keep three significant figures as with multiplication? Or is there a different rule for this? How would I do this for functions in general that are not directly addition/subtraction or multiplication/division? I just realized that none of my physics or math books explains this. I also realized that all these years, I've been taking trig functions and other types of functions for granted when calculating significant figures.