In all measurements, the results of rounding calculations performed fairly complex calculations inevitably there is a particular deviation.To assess this error is common to use two indicators - an absolute and relative error.
If the exact value of the number to subtract the result, we obtain the absolute deviation (and the calculation of a larger number of lower-consuming).For example, if the round in 1370 and 1400, the absolute error will be 1400-1382 = 18. When rounding to 1380, the absolute deviation will be 1382-1380 = 2. The formula takes the form of the absolute error:
Δx = | x * - x|, here
x * - the true value,
x - approximate value.
However, to characterize the accuracy of this figure is not enough.Judge for yourself if the error weight is 0.2 grams, then the weighing of chemicals for the mikrosinteza it will be very much at the weigh 200 grams of sausage is quite normal, and in the measurement of the weight of the railroad car and it all can be seen.So often indicated with absolute or relative error is also calculated.The formula looks like this figure:
δx = Δx / | x * |.
Consider an example.Let the total number of students at the school anyway 196. Rounded this value to 200.
absolute deviation of 200 - 196 = 4. Relative error will be rounded up or 4/196, 4/196 = 2%.
Thus, if we know the true meaning of a certain value, the relative error of the received approximate value is the ratio of the absolute deviation of the approximate value of the exact value.But in most cases to identify the true current value is very difficult and sometimes even impossible.And, therefore, it is impossible to calculate the exact value of the error.Nevertheless, it is always possible to define a number that will always be slightly greater than the maximum absolute or relative error.
example, weighs a melon seller on the beam balance.This is the smallest weight is 50 grams.Libra 2000 grams.This is an approximate value.The exact weight of the melon is unknown.However, we know that the absolute error can not be more than 50 grams.Then the relative error of measurement of weight does not exceed 50/2000 = 2.5%.
value is initially greater than the absolute error, or in the worst case it is equal, is called absolute error limit or the limit of absolute error.In the previous example, the figure is 50 grams.Similarly, determined and limiting relative error, which in the example above was 2.5%.
value of the accuracy limit is not strictly specified.So, instead of 50 grams we might take any number greater than the weight of the smallest weights, say 100 g or 150 g, however, in practice, the minimum value is chosen.And if it is possible to determine exactly what it is at the same time serve as a marginal error.
It so happens that the absolute maximum error is not specified.Then we must assume that it is equal to half of the last unit of this discharge (if a number) or the minimum unit of division (if the instrument).For example, for the millimeter range, this parameter is 0.5 mm, and 3.65 for the approximate number of absolute limit deviation is 0.005.
