Error Calculation Division
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or more quantities, each with their individual uncertainties, and then combine the information from these quantities in order to come up with a final result of our experiment. How can you state your answer for the combined result of these measurements and their uncertainties scientifically? The answer to this fairly common question depends on how the individual measurements error propagation for addition are combined in the result. We will treat each case separately: Addition of measured quantities If you propagation of error division have measured values for the quantities X, Y, and Z, with uncertainties dX, dY, and dZ, and your final result, R, is the sum or difference of error propagation product these quantities, then the uncertainty dR is: Here the upper equation is an approximation that can also serve as an upper bound for the error. Please note that the rule is the same for addition and subtraction of quantities. Example: Suppose we have propagation of uncertainty multiplication and division measured the starting position as x1 = 9.3+-0.2 m and the finishing position as x2 = 14.4+-0.3 m. Then the displacement is: Dx = x2-x1 = 14.4 m - 9.3 m = 5.1 m and the error in the displacement is: (0.22 + 0.32)1/2 m = 0.36 m Multiplication of measured quantities In the same way as for sums and differences, we can also state the result for the case of multiplication and division: Again the upper line is an approximation and the lower line is the exact result
Error Calculation Physics
for independent random uncertainties in the individual variables. And again please note that for the purpose of error calculation there is no difference between multiplication and division. Example: We have measured a displacement of x = 5.1+-0.4 m during a time of t = 0.4+-0.1 s. What is the average velocity and the error in the average velocity? v = x / t = 5.1 m / 0.4 s = 12.75 m/s and the uncertainty in the velocity is: dv = |v| [ (dx/x)2 + (dt/t)2 ]1/2 = 12.75 m/s [(0.4/5.1)2 + (0.1/0.4)2]1/2 = 3.34 m/s Multiplication with a constant What if you have measured the uncertainty in an observable X, and you need to multiply it with a constant that is known exactly? What is the error then? This is easy: just multiply the error in X with the absolute value of the constant, and this will give you the error in R: If you compare this to the above rule for multiplication of two quantities, you see that this is just the special case of that rule for the uncertainty in c, dc = 0. Example: If an object is realeased from rest and is in free fall, and if you measure the velocity of this object at some point to be v = - 3.8+-0.3 m/s, how long has it been in free fall? Answer: we can calculate the time as (g = 9.81 m/s2 is assumed to be known exactly) t = - v / g = 3.8 m/s / 9.81 m/s2 = 0.387 s The uncertainty in th
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Error Calculation Chemistry
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metres long, but I’ve only got a 4 metre tape measure. I’ve also got a 1 metre ruler as well, http://www.math-mate.com/chapter34_4.shtml so what I do is extend the tape measure to measure 4 metres, and then I measure the last metre with the ruler. The measurements I get, with their errors, are: Sponsored Links Now I want to know the entire length of my room, so I need to add these two numbers together – 4 + 1 error calculation = 5 m. But what about the errors – how do I add these? Adding and subtracting numbers with errors When you add or subtract two numbers with errors, you just add the errors (you add the errors regardless of whether the numbers are being added or subtracted). So for our room measurement case, we need to add the error calculation division ‘0.01m’ and ‘0.005m’ errors together, to get ‘0.015 m’ as our final error. We just need to put this on the end of our added measurements: You can show how this works by considering the two extreme cases that could happen. Say the measurement with our tape measure was over by the maximum amount – when we measured 4 m it was actually 3.99 m. Let’s also say that the ruler measurement was over as well by the maximum amount – so when we measured 1.00 m it was really 0.995 m. If we add these two amounts together, we get: This number is exactly the same as the lower limit of our error estimate for our added measurements: You’d find it would also work if you considered the opposite case – if our measurements were less than the actual distances. Adding or subtracting an exact number The error doesn’t change when you do something like this: Multiplication or division by an exact number If you have an exact n