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  Some numerical statements are exact: Mary has 3 brothers, and    2 + 2 = 4. However, all measurements have some degree of uncertainty that may come from a variety of sources. The process of evaluating this uncertainty associated with a measurement result is often called uncertainty analysis or error analysis.

The complete statement of a measured value should include an estimate of the level of confidence associated with the value. Properly reporting an experimental result along with its uncertainty allows other people to make judgments about the quality of the experiment, and it facilitates meaningful comparisons with other similar values or a theoretical prediction. Without an uncertainty estimate, it is impossible to answer the basic scientific question: "Does my result agree with a theoretical prediction or results from other experiments?" This question is fundamental for deciding if a scientific hypothesis is confirmed or refuted.

When we make a measurement, we generally assume that some exact or true value exists based on how we define what is being measured. While we may never know this true value exactly, we attempt to find this ideal quantity to the best of our ability with the time and resources available. As we make measurements by different methods, or even when making multiple measurements using the same method, we may obtain slightly different results. So how do we report our findings for our best estimate of this elusive true value? The most common way to show the range of values that we believe includes the true value is:

measurement = best estimate ± uncertainty

Here are some typical uncertainties of various laboratory instruments:

Meter stick: ± 0.02cm

Vernier caliper: ± 0.01cm

Triple-beam balance: ± 0.02g

Text Provided by UNC Physics Department 

Percent Uncertainty 

When dealing with multiple uncertainties then it is important to determine how  much a single measurement can effect the overall outcome, more on determining overall error in total percent uncertainty.