This is incorrect. The formula for area is A = s2. The differential of the area would be dA = (dA/ds) * ds ≈ dA/ds * Δs.adomad123 said:Homework Statement
Use Differentials to show that an error of 2% in the measurement of the side of a square results in an error of approximately 4% in the calculation of the area
Homework Equations
I'm using Area =(sΔx)^2
adomad123 said:The Attempt at a Solution
Using Δx=0.02,
Area= [itex]s^{2}[/itex][itex]0.02^{2}[/itex] =[itex]s^{2}[/itex]/2500=0.04%[itex]\times[/itex][itex]s^{2}[/itex]
adomad123 said:Homework Statement
Use Differentials to show that an error of 2% in the measurement of the side of a square results in an error of approximately 4% in the calculation of the area
Homework Equations
I'm using Area =(sΔx)^2
The Attempt at a Solution
Using Δx=0.02,
Area= [itex]s^{2}[/itex][itex]0.02^{2}[/itex] =[itex]s^{2}[/itex]/2500=0.04%[itex]\times[/itex][itex]s^{2}[/itex]
Ray Vickson said:Do you really not know the difference between 4% and .04% ?
DE stands for "difference or error". It is a mathematical calculation used to compare two values and determine the difference or error between them. To show error percentage, you would use the formula: (|Actual Value - Expected Value| / Expected Value) * 100.
DE allows scientists to quantify the difference between their experimental results and the expected results. This can help identify areas for improvement or potential sources of error in the experiment.
A higher error percentage indicates a larger difference between the actual and expected values, while a lower error percentage suggests a smaller difference. Ideally, the error percentage should be as close to 0% as possible, indicating a minimal difference between the two values.
Yes, DE does not take into account the direction of the error. In other words, a positive or negative error will have the same effect on the error percentage, even though they may have different implications for the experiment. Additionally, DE assumes that the expected value is the correct value, which may not always be the case.
Yes, there are other methods such as percentage error, mean absolute percentage error, or root mean squared error. Each method has its own advantages and limitations, and the choice of which to use will depend on the specific context and purpose of the experiment.