Multiple roundings can yield an accumulation of errors.
Yes, indeed.
retain a few more digits than what your input quantities have
Excellent advice. Those are called _guard digits_.
then round off to the correct number of significant digits only in your final result.
Sorry, no, that is terrible advice.
There is no such thing as a "final" result, unless you think that your results will never be used for any serious purpose. If you are part of a team, your "final" result is somebody else's initial input, so rounding off your final result is just as disastrous as any other roundoff error.
Keep in mind that roundoff error is an error.
As another way of saying it: There is no such thing as a "correct number of significant digits".
Specific suggestions: "Sig figs" should not be used for anything, ever. They should not even be mentioned in the book, not in section 1.7 or elsewhere. Section 1.7 should be renamed "Uncertainty" or some such.
See item #101 for a catalog of related issues.
In section 1.7 on page 18 it says:
Yes, indeed.
Excellent advice. Those are called _guard digits_.
Sorry, no, that is terrible advice.
There is no such thing as a "final" result, unless you think that your results will never be used for any serious purpose. If you are part of a team, your "final" result is somebody else's initial input, so rounding off your final result is just as disastrous as any other roundoff error.
Keep in mind that roundoff error is an error.
As another way of saying it: There is no such thing as a "correct number of significant digits".
Specific suggestions: "Sig figs" should not be used for anything, ever. They should not even be mentioned in the book, not in section 1.7 or elsewhere. Section 1.7 should be renamed "Uncertainty" or some such.