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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.

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.

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.

Absolute uncertainty is the plus-or-minus amount attached to a measured quantity and is written in the same units as that quantity. Relative uncertainty expresses the uncertainty as a fraction or percentage of the measured value, obtained by dividing the absolute uncertainty by the measured quantity, making it dimensionless.

Conditions: Applies to a measured quantity with a nonzero value when forming the relative ratio.; The absolute uncertainty is expressed in the same units as the measured quantity.

Absolute uncertainty is the plus-or-minus amount attached to a measured quantity and is written in the same units as that quantity. Relative uncertainty expresses the uncertainty as a fraction or percentage of the measured value, obtained by dividing the absolute uncertainty by the measured quantity, making it dimensionless.

Conditions: Applies to a measured quantity with a nonzero value when forming the relative ratio.; The absolute uncertainty is expressed in the same units as the measured quantity.