Percentage Error Combination
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dividing Is one result consistent with another? What if there are several measurements of the same quantity? How can one estimate the uncertainty of a slope on a graph? Uncertainty in a single measurement Bob weighs himself uncertainty calculation formula on his bathroom scale. The smallest divisions on the scale are 1-pound
How To Calculate Percentage Uncertainty
marks, so the least count of the instrument is 1 pound. Bob reads his weight as closest to the how to calculate uncertainty in physics 142-pound mark. He knows his weight must be larger than 141.5 pounds (or else it would be closer to the 141-pound mark), but smaller than 142.5 pounds (or else it would be
How To Calculate Absolute Uncertainty
closer to the 143-pound mark). So Bob's weight must be weight = 142 +/- 0.5 pounds In general, the uncertainty in a single measurement from a single instrument is half the least count of the instrument. Fractional and percentage uncertainty What is the fractional uncertainty in Bob's weight? uncertainty in weight fractional uncertainty = ------------------------ value for weight 0.5 pounds = ------------- = 0.0035 propagation of error division 142 pounds What is the uncertainty in Bob's weight, expressed as a percentage of his weight? uncertainty in weight percentage uncertainty = ----------------------- * 100% value for weight 0.5 pounds = ------------ * 100% = 0.35% 142 pounds Combining uncertainties in several quantities: adding or subtracting When one adds or subtracts several measurements together, one simply adds together the uncertainties to find the uncertainty in the sum. Dick and Jane are acrobats. Dick is 186 +/- 2 cm tall, and Jane is 147 +/- 3 cm tall. If Jane stands on top of Dick's head, how far is her head above the ground? combined height = 186 cm + 147 cm = 333 cm uncertainty in combined height = 2 cm + 3 cm = 5 cm combined height = 333 cm +/- 5 cm Now, if all the quantities have roughly the same magnitude and uncertainty -- as in the example above -- the result makes perfect sense. But if one tries to add together very different quantities, one ends up with a funny-looking uncertainty. For example, suppose that Dick balances on his head a flea (ick!) i
just how much the measured value is likely to deviate from the unknown, true, value of the quantity. The art of estimating
Percentage Uncertainty Physics
these deviations should probably be called uncertainty analysis, but for historical reasons is
Error Propagation Average
referred to as error analysis. This document contains brief discussions about how errors are reported, the kinds of errors uncertainty calculator that can occur, how to estimate random errors, and how to carry error estimates into calculated results. We are not, and will not be, concerned with the “percent error” exercises common in http://spiff.rit.edu/classes/phys273/uncert/uncert.html high school, where the student is content with calculating the deviation from some allegedly authoritative number. Significant figures Whenever you make a measurement, the number of meaningful digits that you write down implies the error in the measurement. For example if you say that the length of an object is 0.428 m, you imply an uncertainty of about 0.001 m. To record this measurement http://www.owlnet.rice.edu/~labgroup/pdf/Error_analysis.htm as either 0.4 or 0.42819667 would imply that you only know it to 0.1 m in the first case or to 0.00000001 m in the second. You should only report as many significant figures as are consistent with the estimated error. The quantity 0.428 m is said to have three significant figures, that is, three digits that make sense in terms of the measurement. Notice that this has nothing to do with the "number of decimal places". The same measurement in centimeters would be 42.8 cm and still be a three significant figure number. The accepted convention is that only one uncertain digit is to be reported for a measurement. In the example if the estimated error is 0.02 m you would report a result of 0.43 ± 0.02 m, not 0.428 ± 0.02 m. Students frequently are confused about when to count a zero as a significant figure. The rule is: If the zero has a non-zero digit anywhere to its left, then the zero is significant, otherwise it is not. For example 5.00 has 3 significant figures; the number 0.0005 has only one significant figure, and 1.0005 has
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