I’m confused as to how, when and why I’m supposed to use significant digits vs when to carry all the decimals my calculator spits out. This is for surveying/civil engineering related fields in particular. My professor has covered both topics extensively but didn’t do a very good job explaining when said rules apply.
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Always carry the full values of your calculator when doing all operations. Rounding to a certain number of sig figs is a last-step action once you have the answer you’re looking for. The point of sig figs is to show to others how confident you are in the accuracy of a *final answer* you are giving, not of every intermediary step of your process.
If you have a notebook full of calculations for a specific engineering problem, think of enclosing that notebook in a black box, where only the measurements you put in and the start and the final answer are visible. This black box is essentially asking the question, “If I put in XYZ values, what is the answer?” What happens inside the black box, as far as finding the un-rounded answer goes, does not matter.
Once you get an un-rounded answer, you analyze the way you combined XYZ inside your black box to determine how many sig figs your answer should have, and you clip your final answer based on that. This is what sig figs rules are for, they take all of the loss of precision of your black box and wrap it into a simple operation you can apply at the very end to safely account for all of it.
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