vertices are stored as 32bit floats (as with all other geometry storage in Blender).
There are no really good ways to see exact floating point values of a vertex in the user interface, Your best option is to print the value in Python.
This behavior is intentional, lots of common values like
0.1 will end up displaying as
For typical usage this isn't helpful.
As a workaround you could scale the object up 100.0x and then set 'Global' in the transform panel, so there is more floating point precision shown though this is not an ideal solution, it may be handy in a few cases.
See also: Video explaining floating point precision - gives some insights as to why this isn't as trivial as you might want/expect.