Percentage uncertainty

The uncertainty in the product, 200 calories, is not simply the sum of the uncertainties in the factors, 0.4°C and 2 grams. Instead, the sum of the percentage uncertainties in the factors determines the uncertainty in a product or a quotient. Fortunately, there is an easy method for estimating it roughly without calculating percentages. This method, based upon the number of figures written, is described in Section 1-2.5. 

The calculation based upon percentage uncertainty is presented in Appendix 4 of the Laboratory Manual. 

Estimate the maximum percentage uncertainty in the measured viscosity of the sample for each of the three data points. 

For example, if the overall percentage uncertainty in current due to readability and indicated error is 5 % and that due to voltage is 3 %, then ARmax= 0.08 R and ARrms=+0.058 R, the latter being smaller in magnitude. 

Calculate the volume of the 0.01 NaOH in problem 1 during which the indicator would change color in each case if the color change observed occurs over 1.0 pH unit. Express this as a percentage uncertainty in the total titration. 

The absolute uncertainty is often converted to a percentage uncertainty. For the example, this would be 25.4 s 0.4% since 100 = 0.4%. ... 

Note that uncertainties are themselves approximate and are generally not reported to more than one significant figure, so the percentage uncertainty is reported as 0.4%, not 0.39370%. 

When raising to the nth power, multiply the percentage uncertainty by n. When extracting the nth root, divide the percentage uncertainty by n. 

Propagation of uncertainties in processed data, and percentage uncertainties... 

Calculate the mass of hydrated copper(ii) sulfate and determine the percentage uncertainty in its mass. Mass of hydrated copper(ii) sulfate crystals weighed = (1.500 0.002)g... 

Absolute value calculation Percentage uncertainty determination... 

Then in terms of the percentage uncertainty in carrier densities, flie values are some 38.6 times the uncertainties in the potential. For this example an uneertainty in the potential of 0.00517 corresponds to about a 20% uncertainty in the carrier densities at the worst case point. This may still represent a very small percentage of the maximum carrier densities in the structure as the point where this occurs is deep within the depletion region where Poisson s equation is dominated not by the free carriers but by the fixed impurity charge density. This is the reason an accurate value of the potential can be obtained even in the presence of a rather high uncertainty in the free carrier densities - they are small contributions to Poisson s equation around the p-n junction interface. However, it is important to understand the accuracy with which any solution to a PDE can be obtained by any numerical technique. 

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