Information on Extended Precision
[Text provided by David on 10-11-2013]

What does this setting do?

Saving with Extended Precision saves values with an additional six digits, 18 instead of 12 digits.

Why should I check this box?

If this is an optimization model or you plan to convert it to an optimization model in the future, you must save with extended precision.

Why is this necessary for Optimization?

When models are saved, there is roundoff error in the last few digits of every numeric value. Roundoff error has little effect during simulation, but in Optimization, it can become very significant in the matrix computations and cause numerical instability. When a model is consistently saved with extended precision, the roundoff error takes place at such small magnitudes that it becomes inconsequential even for optimization. Thus, if a model is going to be used for optimization at any point in the future, extended precision should always be used.

How does this manifest into problems?

One of the most common places that roundoff error creates problems in optimization is slot minimum and maximum values. Once saved, this roundoff error is generally preserved in the model far into the future and can cause errors that are difficult to debug.

Can I decide this later?

Saving later with extended precision doesn't remove the existing roundoff errors, but it does prevent creating new roundoff errors. Removing roundoff error requires editing of the slot values. Saving later without extended precision truncates values and is OK for non-optimization models.