The value in the parentheses is the symmetric one-sigma bound. If I say the atomic weight of F is 18.998403163(6) g/mol... mean 18.998403163 g/mol std

The value in the parentheses is the symmetric one-sigma bound. If I say the atomic weight of F is 18.998403163(6) g/mol... mean 18.998403163 g/mol std.dev. 0.000000006 g/mol If I say Planck time is 5.391245(60)e−44 s... mean 5.391245e−44 s std.dev. 0.000060e-44 s The standard rules for rounding imply that whenever a measurement is given to a certain number of significant figures, you're leaving out "0(5)" from the end. So 1.2345 is 1.23450(5) in parenthetical notation. Significant figures rules give you a close-enough propagation of error, but in order to be more exact, you need to combine absolute uncertainties when adding or subtracting, and combine relative uncertainties when multiplying or dividing.