# Thread: Absolute Error and Relative Error

1. ## Absolute Error and Relative Error

How do you find absolute and relative error?

For example, one of my homework problems:

Find the linear approximation to f(x)=ex at x=0 and use it to appoximate e0.1. My answers were x+1 and 1.01. I also had to use x+1 to approximate e-0.25 which I got 0.75. I also have to find the absolute and relative error. How would I do this? And which is closer to its corresponding actual value? Why?

2. ## Re: Absolute Error and Relative Error

Absolute error is (correct value - estimate), and relative error is (correct value - estimate)/(correct value). For example, if you estimate a distance as 500 miles and the actual value is 505 miles, your absolute error is 5 miles, and your relative error is 5/505 = 0.99%.

Approximations (linear or otherwise) are typically less accurate when they're further away from the known value. So I would expect the relative error to be greater at -0.25 than at 0.1. I didn't do the calculation, though.

- Hollywood