If one wants to export/reimport in MIF format, one must make sure of the precision with which the coordinates are written down. The number of decimals must be such that they correspond to the level of precision of the map before exporting. In an unbounded UTM projection, the precision is 1 cm less a micron in Latitude (just over 10,000 km for 1 billion positions) and about double in the X direction. Because of possible roundings, if one wants the full guarantee of not losing information by giving the same coordinates to 2 distinct points, one would require coordinates posted in millimeters.
MapInfo Pro is responsive to precision settings. An example of this would be an MTM (Modified Transverse Mercator) table without specific bounds, its object location (with the ObjectInfo window) and its exported coordinates in cms (2 decimals with a metric standard). If using a bounded map definition, they are in millimeters. However, there is no difference when the bounds width varies; at 2000000 meters (internal precision 1 mm) or at 200 000, there are only 3 decimal digits.