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Multiplication and Division: Carry the result only to the same number of significant digits which the number in the calculation with the least number of significant digits has. Example: 45.73 × 2.56 = 117.0688 = 117. 45.73 has four significant digits while 2.56 has only three, therefore the result has three significant digits. Propagation of Error When doing calculations on data with uncertainties in it, the uncertainties must be taken into account. Typically this is done using either simple averages or standard deviations of errors. In general, the relative errors add up to give a total error that is reported as: Basic Rules Addition and Subtraction: For an equation, z = x + y –z, uncertainty can be determined one of the following ways: Multiplication and Division: For multiplication by an exact number, multiply the uncertainty by the same number:
58 For numbers containing uncertainties: Products of Powers