I am not very new to electronics but new here.

I have been doing electronics in the past but in a very practical way, not dealing with any kind of theory and calculation. Lately, I have been studying some mathematics, physics, and some theory of electronics and so I'm calculating some things.

I am familiar with how to round numbers off for example when you're solving a physics or chemistry problem, rounding numbers off, significant digits and the whole story but it seems to me that that method simply does not work too well in electronics. Most of the time, if you round your numbers off based on the number of significant digits, you'll get numbers that make no practical or logical sense. Although, reading some books and trying to solve the examples therein, it's hard to know how many significant digits to assume in the first place.

Now my question is, how does an electrical engineer or electronics engineer normally deal with his numbers? I have read on some website that engineering is an "art" and that you should deal with numbers based on the situation and that, you'll learn how to do it after you've gathered some experience and "intuition." I do not know how true that could be.

I really would not mind even very comprehensive answers here even if you happen to kindly provide me with a whole pdf book to go through.

Another way that would help me clear my doubts here is if you would solve a typical problem somewhat more complicated and calculation-involved than the Ohm's law and explain how you do it step by step and what you assume each step of the way while solving the problem. Your help would be greatly appreciated.

Thank you!