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Precision help needed *ASAP* - Thanks


Any help, or insight would be appreciated. I can be reached at Please be considerate since I am no expert, I'm just
a guy who is trying to solve for a problem

My problem is relatively simple and common but the solution escapes me
if there is one at all.

Within a limited precision say 20 digits, I have to invert my results
several times, and sometimes back again BUT;

1 / x = 0.5624136....3233
1 / 0.5624136....3233 = x is not happening. 

I know this is the result of rounding error, but as an accumulative
process it really makes my life harder, since I have no way of knowing
how the result was numbered.

So my question is:

How do I compensate in result of 1/x so that when I try to go back I do
get my x, without keeping a list of things to do at each step.

Again - a million thanks for any insight/help. I am using Mathematica
2.2 on a very old Mac.

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