The percent error is a special case of the percentage form of relative change calculated from the absolute change between the experimental (measured) and theoretical (accepted) values, and dividing by the theoretical (accepted) value.
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The terms "Experimental" and "Theoretical" used in the equation above are commonly replaced with similar terms. Other terms used for experimental could be "measured," "calculated," or "actual" and another term used for theoretical could be "accepted." Experimental value is what has been derived by use of calculation and/or measurement and is having its accuracy tested against the theoretical value, a value that is accepted by the scientific community or a value that could be seen as a goal for a successful result.
Although it is common practice to use the absolute value version of relative change when discussing percent error, in some situations, it can be beneficial to remove the absolute values to provide more information about the result. Thus, if an experimental value is less than the theoretical value, the percent error will be negative. This negative result provides additional information about the experimental result. For example, experimentally calculating the speed of light and coming up with a negative percent error says that the experimental value is a velocity that is less than the speed of light. This is a big difference from getting a positive percent error, which means the experimental value is a velocity that is greater than the speed of light (violating the theory of relativity) and is a newsworthy result.
The percent error equation, when rewritten by removing the absolute values, becomes:
It is important to note that the two values in the numerator do not commute. Therefore, it is vital to preserve the order as above: subtract the theoretical value from the experimental value and not vice versa.
Read more about this topic: Relative Change And Difference
Famous quotes containing the words percent and/or error:
“Don’t forget what I discovered—that over ninety percent of all national deficits from 1921 to 1939 were caused by payments for past, present, and future wars.”
—Franklin D. Roosevelt (1882–1945)
“They have their belief, these poor Tibet people, that Providence sends down always an Incarnation of Himself into every generation. At bottom some belief in a kind of pope! At bottom still better, a belief that there is a Greatest Man; that he is discoverable; that, once discovered, we ought to treat him with an obedience which knows no bounds. This is the truth of Grand Lamaism; the “discoverability” is the only error here.”
—Thomas Carlyle (1795–1881)