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When precise computations are necessary, consider alternative representions representations that may be able to completely represent your values. For example, if you are doing arithmetic on decimal values and need an exact rounding mode based on decimal values, represent your values in decimal instead of using floating point, which uses binary representation.
When precise computation is necessary, carefully and methodically evaluate the commulative cumulative error of the computations, regardless of whether decimal or binary is used, to ensure that the resulting error is within tolerances. Consider using numerical analysis to properly understand the numerical properties of the problem.