Question

the dimensions of a rectangle are measured to be 12.2 inches by 11.8 inches. the actual dimensions are 12.3 inches by 11.9 inches. what is the relative error

Answer 1

Relative error is the ratio of the error to the size. In this case, the sizes are about the same, but I choose the smaller, since the errors are both a tenth of an inch. This will give me a slightly larger result, and more conservatively represents the relative error estimate. So,\[\frac{.1}{11.9}=\frac{1}{119} \approx 0.84 ~percent\]Note that the error was positive in one case, and negative in the other. Unless it is uniformly one way or the other, use the absolute value of the error.