The error or deviation is divided by the nominal value and the resulting fraction is multiplied by 100%.
The whole amount of something is always 100% of it. It is often convenient to represent an error or deviation as some fraction of the whole amount. It is often easier to deal with numbers in the range 0-100 than with numbers less than 1. Expressing error or deviation fractions as a percentage accomplishes all of this. Example My budget is 50, and I spent 55. Rather than report both those numbers, it is convenient to say I went over budget by 10%. (The error amount, 5, may be uninformative by itself. It might be considered irrelevant "pocket change" in comparison to a budget of 50,000. It might represent gross malfeasance in relation to a budget of 1 or 2.) Many of us, especially in the engineering professions, learn quickly what percentage deviations are significant and what are not. When an allowed tolerance is .001%, a deviation of .01% is completely unacceptable. In many other instances, meeting a requirement within 10% is "close enough" due to the nature of the estimates involved or because of the margin or (lack of) sensitivity of the system.
The whole amount of something is always 100% of it. It is often convenient to represent an error or deviation as some fraction of the whole amount. It is often easier to deal with numbers in the range 0-100 than with numbers less than 1. Expressing error or deviation fractions as a percentage accomplishes all of this. Example My budget is 50, and I spent 55. Rather than report both those numbers, it is convenient to say I went over budget by 10%. (The error amount, 5, may be uninformative by itself. It might be considered irrelevant "pocket change" in comparison to a budget of 50,000. It might represent gross malfeasance in relation to a budget of 1 or 2.) Many of us, especially in the engineering professions, learn quickly what percentage deviations are significant and what are not. When an allowed tolerance is .001%, a deviation of .01% is completely unacceptable. In many other instances, meeting a requirement within 10% is "close enough" due to the nature of the estimates involved or because of the margin or (lack of) sensitivity of the system.
