I was taught that when adding/subtracting measurements, add the absolute uncertainties, and when multiplying/dividing measurements, add the relative uncertainties.
I have a problem in a lab where I need to find the difference between two measurements that are very close together, and are each very precise; however, when I propagate the absolute uncertainties, I get a huge relative uncertainty for the final result (upwards of 50%). Here it is:
(0.050 ± 5%) - (0.044 ± 3%) = ? = (0.050 - 0.044) ± ((0.050 * 5/100) + (0.044 * 3/100)) = 0.006 ± 0.00382
This ± 0.00382 corresponds to 63.7% relative uncertainty; am I doing something wrong? Both of the original measurements were pretty accurate (<12% RU). In this case can I just add their relative uncertainties instead of converting to absolute, which is very large in comparison with the difference between the measurements?