What can an ArcGIS user modify to increase the numeric precision used to store coordinate values?

Increasing the numeric precision used to store coordinate values in ArcGIS can be achieved by modifying the X,Y Resolution. This parameter determines the smallest unit of measurement that can be represented in the coordinate system. A higher resolution allows for finer distinctions between coordinate values, which directly increases the precision of the stored coordinates.

When the X,Y Resolution is set to a smaller value, it enables the system to record more detailed positional information, thus providing enhanced accuracy when mapping or analyzing spatial data. For instance, if the resolution is set too high, it may lead to rounding errors or a lack of detail in the representation of features.

Other options, while relevant to coordinate systems, do not fundamentally control the precision of coordinate storage in the same way. The X,Y Tolerance is more related to how close two features must be to be considered as coincident rather than affecting precision directly. The Z value relates to elevation measurements and the M Value is used for measuring non-spatial attributes along a line, which are not primarily concerned with the basic numeric precision of the X and Y coordinates. Thus, focusing on X,Y Resolution is the correct approach to achieve a higher numeric precision in coordinate representation.