DocumentationMathematicaBuilt-in FunctionsNumerical ComputationNumerical Precision
Further Examples: SetAccuracy
When an expression contains machine-precision real numbers Mathematica tries to do all computations with machine precision.
This causes a loss of accuracy. One of the summands had an accuracy of but the result has a much lower accuracy.
By raising the accuracy of each subexpression, you can increase the accuracy of the overall result.
Adding two numbers of the same accuracy gives a result which is less accurate by one binary bit.