When you create a part in the Part module, it exists in its own coordinate system, independent of other parts in the model. In contrast, when you create an instance of the part in the Assembly module and position it relative to other part instances, you are working in the assembly's global coordinate system.
To preserve precision, the Mesh module separates the positioning information of a part instance from the geometry of the instance. As a result, when you generate a mesh, the nodal coordinates for the part instance are computed relative to the coordinate system of the original part. (When the Job module generates an input file, Abaqus/CAE writes the nodal coordinates for each instance relative to its own coordinate system and passes the instance positioning and orientation information to the analysis product via the *INSTANCE keyword.)
The Mesh module stores these nodal coordinates in single precision. If the geometry of the part lies far from the origin of its coordinate system, some precision of the nodal coordinates will be lost. To prevent this loss of precision, you should try to position a part close to the origin of its coordinate system. For example, the origin of the coordinate system of an Abaqus/CAE native part is located at the origin of the sketch that defined the base feature. Therefore, if possible, you should position the sketch of the base feature over the origin of the sketcher grid.