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The significance of Error and Uncertainty in real mathematical world

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There is no denying the fact that  all readings, data, results or other numerical quantities taken from the real world by direct measurement or otherwise are subject to uncertainty. This is a consequence of not being able to measure anything exactly. Uncertainty cannot be avoided but it can be reduced by using 'better' apparatus. The uncertainty on a measurement has to do with the precision or resolution of the measuring instrument. When results are analyzed it is important to consider the affects of uncertainty in subsequent calculations involving the measured quantities. If you are unlucky (or careless) then your results will also be subject to errors. Errors are mistakes in the readings that, had the experiment been done differently, been avoided. It is perfectly possible to take a measurement accurately and erroneously! Unfortunately it is not always possible to know when you are making an error (otherwise you wouldn't make it!) and so good experimental technique