Propagation Of Error Multiply By Constant
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would be your guess: can an American Corvette get away if chased by an Italian police Lamborghini?
The top speed of the CorvetteError Propagation Calculator
is 186 mph ± 2 mph. The top speed of the Lamborghini Gallardo error propagation physics is 309 km/h ± 5 km/h. We know that 1 mile = 1.61 km. In order to convert the speed of
Error Propagation Inverse
the Corvette to km/h, we need to multiply it by the factor of 1.61. What should we do with the error? Well, you've learned in the previous section that when you multiply two quantities, error propagation square root you add their relative errors. The relative error on the Corvette speed is 1%. However, the conversion factor from miles to kilometers can be regarded as an exact number.1 There is no error associated with it. Its relative error is 0%. Thus the relative error on the Corvette speed in km/h is the same as it was in mph, 1%. (adding relative errors: 1% + 0% = 1%.) It error propagation chemistry means that we can multiply the error in mph by the conversion constant just in the same way we multiply the speed. So our answer for the maximum speed of the Corvette in km/h is: 299 km/h ± 3 km/h. Now we are ready to answer the question posed at the beginning in a scientific way. The highest possible top speed of the Corvette consistent with the errors is 302 km/h. The lowest possible top speed of the Lamborghini Gallardo consistent with the errors is 304 km/h. Bad news for would-be speedsters on Italian highways. No way can you get away from that police car. The rule we discussed in this chase example is true in all cases involving multiplication or division by an exact number. You simply multiply or divide the absolute error by the exact number just as you multiply or divide the central value; that is, the relative error stays the same when you multiply or divide a measured value by an exact number. << Previous Page Next Page >> 1 For this example, we are regarding the conversion 1 mile = 1.61 km as exact. Actually, the conversion factor has more significant digits. Home - Credits - Feedback © Columbia University
find that the error in this measurement is 0.001 in. To find the area we multiply the width (W)
Multiplying Uncertainties
and length (L). The area then is L x W error propagation average = (1.001 in) x (1.001 in) = 1.002001 in2 which rounds to 1.002 in2. This gives an error
Error Propagation Definition
of 0.002 if we were given that the square was exactly super-accurate 1 inch a side. This is an example of correlated error (or non-independent error) since https://phys.columbia.edu/~tutorial/propagation/tut_e_4_3.html the error in L and W are the same. The error in L is correlated with that of in W. Now, suppose that we made independent determination of the width and length separately with an error of 0.001 in each. In this case where two independent measurements are performed the errors are independent or uncorrelated. Therefore the error http://www.utm.edu/~cerkal/Lect4.html in the result (area) is calculated differently as follows (rule 1 below). First, find the relative error (error/quantity) in each of the quantities that enter to the calculation, relative error in width is 0.001/1.001 = 0.00099900. The resultant relative error is Relative Error in area = Therefore the absolute error is (relative error) x (quantity) = 0.0014128 x 1.002001=0.001415627. which rounds to 0.001. Therefore the area is 1.002 in2± 0.001in.2. This shows that random relative errors do not simply add arithmetically, rather, they combine by root-mean-square sum rule (Pythagorean theorem). Let’s summarize some of the rules that applies to combining error when adding (or subtracting), multiplying (or dividing) various quantities. This topic is also known as error propagation. 2. Error propagation for special cases: Let σx denote error in a quantity x. Further assume that two quantities x and y and their errors σx and σy are measured independently. In this case relative and percent errors are defined as Relative error = σx / x,
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