Question

Knowing that the formula of the percent error is theoretical measured x 100, what is the purpose of computing this % theoretical error during any experience? To determine the final answer in percentage. To conclude the difference between the theoretical and actual values The difference between an experimental and theoretical value, divided by the theoretical value, multiplied by 1,000. To gauge how close a measured value is to a true value. The difference between an experimental and theoretical value, divided by the theoretical value, multiplied by 100.

Answer 1

This is the measure of the relative difference between the true and the measured value which is quite often used in computation, especially numerical analysis. So the answer is the fourth option, to gauge how close a measured value is to the actual one.

The idea is to look at the absolute difference (that what the | ... | is for), and then divide by the theoretical value. Say you had two values which were off by say 10^-4, then dividing by the theoretical value acutally keeps the results devoid of the order since that is irrelevant. This divising step is more important for values that are off by an order. And hence the name relative difference.