To calculate the volume, she multiplies together the length, width She measures the length, width, and height: Jane needs to calculate the volume of her pool, so that she knows Simply by adding the uncertainties in the several quantities. When one multiplies or divides several measurements together,įractional (or percentage) uncertainty in the final result In the flea's height in fact, it swamps the flea's own heightĬombining uncertainties in several quantities: multiplying and dividing The uncertainty in Dick's height swamps the uncertainty To express the sum of the two heights is far more than either In technical terms, the number of significant figures required To within a couple of cm, what difference does it make if the If we can't tell exactly where the top of Dick's head is ? combined height = 186.020 cm +/- 2.003 cm ?īut wait a minute! This doesn't make any sense! Uncertainty in combined height = 2 cm + 0.003 cm Using a pair of calipers,ĭick measures the flea to have a height of 0.020 cm +/- 0.003 cm. For example, suppose that Dick balances on his Very different quantities, one ends up with a funny-looking Now, if all the quantities have roughly the same magnitudeĪnd uncertainty - as in the example above - the result Uncertainty in combined height = 2 cm + 3 cm If Jane stands on top of Dick's head, how far is her head One simply adds together the uncertainties to find theĭick and Jane are acrobats. When one adds or subtracts several measurements together, ![]() Percentage uncertainty = - * 100%Ĭombining uncertainties in several quantities: adding or subtracting What is the uncertainty in Bob's weight, expressed as a percentage ![]() What is the fractional uncertainty in Bob's weight?įractional uncertainty =. In general, the uncertainty in a single measurement (or else it would be closer to the 143-pound mark). (or else it would be closer to the 141-pound mark), He knows his weight must be larger than 141.5 pounds The smallest divisions on the scale are 1-pound marks,īob reads his weight as closest to the 142-pound mark. How can one estimate the uncertainty ofīob weighs himself on his bathroom scale.What if there are several measurements of the same quantity?.Is one result consistent with another?.Combining uncertainties in several quantities:.
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