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The relative error is often used to compare approximations of numbers of widely differing size; for example, approximating the number 1,000 with an absolute error of 3 is, in most applications, much worse than approximating the number 1,000,000 with an absolute error of 3; in the first case the relative error is 0.003 and in the second it is only 0.000003.
There are two features of relative error that should be kept in mind. Firstly, relative error is undefined when the true value is zero as it appears in the denominator (see below). Secondly, relative error only makes sense when measured on a [[Level_of_measurement#Ratio_scale|ratio scale]], (i.e. a scale which has a true meaningful zero), otherwise it would be sensitive to the measurement units. For example, when an absolute error in a [[temperature]] measurement given in [[Celsius scale]] is 1 °C, and the true value is 2 °C, the relative error is 0.5, and the percent error is 50%. For this same case, when the temperature is given in [[Kelvin scale]], the same 1 K absolute error with the same true value of 275.15 K gives a relative error of 3.63{{e|-3}} and a percent error of only 0.363%. Celsius temperature is measured on an [[Level_of_measurement#Interval_scale|interval scale]], whereas the Kelvin scale has a true zero and so is a ratio scale. Thus the relative error is not very meaningful.
==Instruments==
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