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For addition and subtraction, the absolute uncertainties of the inputs combine in quadrature. The plus or minus signs in the formula do not matter because they are squared in the propagation equation, resulting in the same rule for both operations.

Conditions: The derived quantity is a sum or difference of two measured variables ($z = \pm x \pm y$).; The variables $x$ and $y$ are independent measured quantities.

For addition and subtraction, the absolute uncertainties of the inputs combine in quadrature. The plus or minus signs in the formula do not matter because they are squared in the propagation equation, resulting in the same rule for both operations.

Conditions: The derived quantity is a sum or difference of two measured variables ($z = \pm x \pm y$).; The variables $x$ and $y$ are independent measured quantities.

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 ($z=\frac{x}{y}$).; 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 ($z=\frac{x}{y}$).; The variables $x$ and $y$ are nonzero so the relative uncertainty ratios are defined.; The uncertainties are treated as independent.