Suppose that a buret is filled with solution to a volume reading of 2.64 mL. Solution is delivered from the buret to a flask. If a number known to 1 part in 100 is multiplied by a number known to 1 part in 1000, the product can be known to at best 1 part in 100. Uncertainty in volume is 0.01 mL, or 1 part in 1000. The volume is less certain than the mass. At best, density is known to about 1 part in 1000.
Precisions carry through calculations according to the same rules.
Frequently we need to take the logarithm of a measured number to make a plot. Comparing with 3.9031, the variation is in the 3rd decimal place. The result is 3.903 0.004. The number of digits following the decimal point in the log is the same as the number of significant figures in the original measured value. This is always true.