Question

Although the textbook uses absolute value bars around the formula for percent error, I suggested that it is usually preferable NOT to use absolute value bars. What extra information are we losing by using the absolute value bars?

Answer 1

If we remove the absolute bars then percentage error can be negative or positive.

in the formula of percentage error, in numerator part we have ( experimental value - actual value ). Then we will have two possibilities -

If our experimental value is less than actual value then the error will be negative, so negative error means there is something which we measured less than the actual.

If our experimental value is more than actual value then the error will be positive, so positive error means there is something which we measured more than the actual or we have just approximated something which affect our result more.

But when we use absolute value we will losse all this information.