For the purposes of CENG 176A/B reports, error should always be reported as (measured value) ± (error), where the error has the same units as the measure value. For simplicity, we'll use the following (conservative) rules regarding significant figures:
For all intermediate calculations, don't round anything.
When you're ready to report a number:
Round the error to one significant figure.
Round and report the measured variable to the same precision as the error.
For example, if the measured value was 22.6654 mL/s and the uncertainty was 1.66 mL/s, we'd first round the uncertainty to 2 mL/s (one significant figure) and then round the measured value to 23 mL/s (same number of decimal points). The measure variable would therefore be reported as 23 ± 2 mL/s.
This is a good general procedure when procedures like regression or propagation of error are involved but it has a few limitations to be aware of (as do most rules for assigning significant figures):
If the error was produced from an instrument for which you're going to estimate error as half the smallest measurement (like a ruler or balance) then you report the measured value to the precision of the instrument along with half the smallest measurement as the uncertainty (in other words, don't round anything). For example, if you're using a balance with four digits of precision (e.g., 0.0000 g) and you measure a sample of 0.0221 g, then you should report this number as 0.0221 +/- 0.00005 g even though that's four digits of precision on the measured value and five digits of precision on the error (normally they'll match). Depending on which reference you read you'll see variations of this kind of rule, which can be annoying.
Occasionally this rule can produce very large errors but that's less of a problem and more of a feature: better to have to think critically about a large error than overlook an inappropriately small error.
This method doesn't work for cases like the LPCVD simulation and liposome nanoparticle analysis because we can't see inside the "black box" of how the machine (or computer program) is calculating its numbers. As with the previous case we simply use our best engineering judgment to report a reasonable number of significant figures.