Calculating errors (propagation)

In summary, error propagation is the process of determining the uncertainty or error in a calculated quantity based on the uncertainties or errors in the measured values used to calculate it. It is important in scientific research as it allows for a better understanding and communication of the level of uncertainty in measurements and calculations. To calculate the error in a sum or difference of quantities, individual errors must be added in quadrature. The rule for calculating the error in a product or quotient of quantities involves adding relative errors in quadrature and then multiplying by the value. Error propagation can be applied to any type of measurement or calculation, as long as uncertainties are understood. Common sources of error in scientific measurements include instrument limitations, human error, environmental factors, and inherent variability in the system
  • #1
pwphysics101
3
0
Completely new to the concept of errors and don't know how to approach this...

Calculate value and error in Z

Z= 2AB^2/C


Where
A= 100 Error in A= +/- 0.1
B= 0.1 Error in B= +/- 0.005
C= 50 Error in C= +/- 2


Plugging in the numbers Z= 0.04

How do you carry the errors over into the equation? I think the answer is suppose to look like (0.04 +/-X.XX)..

Thanks for any help..
 
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  • #2
As I understand it, the error is simply the widest possible range the value of Z could have. This is all I will say.
 

FAQ: Calculating errors (propagation)

What is error propagation and why is it important?

Error propagation is the process of determining the uncertainty or error in a calculated quantity based on the uncertainties or errors in the measured values used to calculate it. It is important because it allows scientists to understand and communicate the level of uncertainty in their measurements and calculations, which is crucial for accurately interpreting and using scientific data.

How do you calculate the error in a sum or difference of quantities?

To calculate the error in a sum or difference of quantities, you must first determine the individual errors or uncertainties associated with each quantity. Then, you can add the individual errors in quadrature (square each error, add them together, and take the square root) to get the total error in the sum or difference.

What is the rule for calculating the error in a product or quotient of quantities?

The rule for calculating the error in a product or quotient of quantities is to add the relative errors (ratio of the error to the value) of each quantity in quadrature, and then multiply by the value of the product or quotient. This means that the relative error increases as the value of the product or quotient increases, highlighting the importance of precise measurements in these calculations.

Can error propagation be applied to any type of measurement or calculation?

Yes, error propagation can be applied to any type of measurement or calculation, as long as there is an understanding of the uncertainties or errors associated with the measured values. It is a fundamental concept in scientific research and is used to ensure the accuracy and reliability of data and results.

What are some common sources of error in scientific measurements?

Some common sources of error in scientific measurements include instrument limitations, human error in reading or recording measurements, environmental factors (such as temperature or humidity), and inherent variability in the system being studied. It is important for scientists to identify and minimize these sources of error in order to obtain more precise and accurate results.

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