You can sometimes ignore the smaller relative uncertainty when one measurement is much more accurate, relatively speaking, than the other. In this case, the combined relative uncertainty is approximately equal to the larger one, and the more accurate measurement behaves as if it were an exact constant.
Conditions: The comparison is between relative uncertainties.; One measurement is much more accurate relative to the other.; The approximation is acceptable for the intended level of precision.
You can sometimes ignore the smaller relative uncertainty when one measurement is much more accurate, relatively speaking, than the other. In this case, the combined relative uncertainty is approximately equal to the larger one, and the more accurate measurement behaves as if it were an exact constant.
Conditions: The comparison is between relative uncertainties.; One measurement is much more accurate relative to the other.; The approximation is acceptable for the intended level of precision.
For products and quotients, the relative uncertainties of the inputs add in quadrature. You calculate the relative uncertainty of the result by taking the square root of the sum of the squared relative uncertainties of the individual variables.
Conditions: The derived quantity is a product (z=xy) or a quotient (z=yx).; The variables x and y are nonzero so the relative uncertainty ratios are defined.; The uncertainties are treated as independent.
For products and quotients, the relative uncertainties of the inputs add in quadrature. You calculate the relative uncertainty of the result by taking the square root of the sum of the squared relative uncertainties of the individual variables.
Conditions: The derived quantity is a product (z=xy) or a quotient (z=yx).; The variables x and y are nonzero so the relative uncertainty ratios are defined.; The uncertainties are treated as independent.