When performing calculations with real numbers, we need to be concerned with the exponential difference between two of them. When one exponent is very large (positive) and the other very small (negative), we will likely produce either insignificant results or a NaN. This happens when the calculated result will either represent an insignificant change to the largest exponent value via addition and subtraction—therefore, precision will be lost—or be outside the possible range of values via multiplication and division—therefore, a NaN will result. Adding a very, very small value to a very, very large value may not give any significant change in the resulting value—again, precision in the result will be lost.
It is only when the exponents are relatively close, and the calculated result is within a reasonable range, that we can be sure of the accuracy of our result.
Granted that with 64-bit integer values and up to 128...
