There are several ways to set bounds to existing and new tables.
The first one would be when creating a new table, as explained below:
Display the MapBasic window in MapInfo Pro and create a mappable table called FOO. You should see this line appear in the MapBasic window:
Create Map for FOO Coordsys Earth Projection 1,0
To set the bounds for this table to 2*2 degrees, ranging from 110-112 degrees Longitude and 41-43 degrees Latitude, position the cursor at the end of the above line and change it to this:
Create Map for FOO CoordSys Earth Projection 1,0 Bounds (110,41)
(112,43)
Do this before adding any objects to FOO because it will delete all existing Map objects, the attribute data remains intact.
The second method is much easier and uses the Utility described in this testplan.
Another technique is to introduce the proper bounds specifications in the header of a MIF file. As many format translators generate MIF files, adding the bounds (either through requests of the translator itself or with a text editor later) is very feasible. For an existing table, exporting it as a MIF file, changing (or adding) the bounds and reimporting it is also possible. In this case, the existing coordinates do not gain in precision; they stay at the level they were before and may even be slightly altered because of the various roundings, but manipulations and creations will benefit from the new precision.