Propagation error in finding the perimeter and area, .

In summary, to measure the size of your back yard, you can use a tape measure with an accuracy of 0.05m. The length of the yard is 8.6m and the width is 7m. To calculate the perimeter, you can use the equation s=square root(changeA)^2+(changeB)^2) and the perimeter is 31.4m. The error in the perimeter is unknown. To calculate the area, you can use the equation A=lw and the area is 60.2m^2. The error in the area is also unknown.
  • #1
megkirch
17
0

Homework Statement


I want to measure the size of my back yard. I estimate that I can measure the length and width of the yard using a tape measure to an accuracy of 0.05m. I find that the length of the yard is 8.6 m and the width is 7 m.



Calculate the perimeter of the yard and its error
Now calculate the area of the yard and its error


Homework Equations


s=square root(changeA)^2+(changeB)^2)


The Attempt at a Solution


I calculated the perimeter and got 31.4m. i can't figure out how to get the error in the perimeter. I thought it would be 8.55(2)+6.95(2) =31.0 -31.4=.4 but its not correct
 
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  • #2
You say your accuracy is 0.05m.

Then the length is 8.60 m. the error in measurement is 0.05m
The width is 7.00m with a measurement error of 0.05m
 

What is propagation error in finding the perimeter and area?

Propagation error in finding the perimeter and area refers to the error that occurs when measurements are taken and calculations are made to determine the perimeter and area of a shape. This error can be caused by rounding errors, measurement inaccuracies, or formula errors.

How does propagation error affect the accuracy of perimeter and area calculations?

Propagation error can greatly affect the accuracy of perimeter and area calculations. Even a small error in measurement or calculation can lead to a significant difference in the final result. This is especially true for shapes with complex or irregular boundaries.

What are some ways to minimize propagation error in finding the perimeter and area?

One way to minimize propagation error is to use more precise measurement tools, such as a digital caliper or laser distance meter. Another way is to use more accurate formulas and double-check all calculations. It is also important to limit the number of rounding steps in the calculations.

How does the shape of an object affect propagation error in finding the perimeter and area?

The shape of an object can greatly affect propagation error. Shapes with more complex or irregular boundaries are more susceptible to error compared to simple shapes like squares or circles. This is because it is more difficult to accurately measure and calculate the perimeter and area of these shapes.

Can propagation error be completely eliminated when finding the perimeter and area?

No, propagation error cannot be completely eliminated. However, it can be minimized by using more accurate measurement tools and formulas, and by double-checking all calculations. It is also important to keep in mind that some level of error is expected in any measurement or calculation process.

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