# The temperature measured in an experiment was "64.9"^@"C". The theoretical temperature is "55.0"^@"C". What is the percent error?

May 2, 2014

Percent error = $| \text{theoretical - experimental"/"theoretical"|}$ x 100

In this example, the theoretical is 55.0 Celsius and the measured is the experimental which is 64.9 Celsius.

The difference in terms of absolute value is 9.9:

$| 55.0 - 64.9 |$ = $9.9$

$| \text{9.9"/"55.0} |$ = $.18$

$.18$ x $100$ = 18 %

The purpose of percent error is to provide a measure of how close you are to an accepted standard.

The error can be attributed to imprecision of instrumentation or due to experimental error or both.

A small percent error such as 5 % validates that the experiment was conducted with precise thermometers or that experimental technique was carefully carried out.

Theoretical values determined after numerous careful experiments are set as a standard value such as the standard kilogram.