I don’t understand your problem. Why do you want to place a point at an arbitrary location, when by your own description, you only need the centerline and the radius. You can do it, but why? Why not just start your circle from origin (i.e. “centerline” of the drawing) and specify your desired radius.
As TigerMike’s drawing clearly shows, the system only displays 3 significant digits (presumably for cosmetic reasons), but it remembers and takes into account the exact dimension entered when calculating things like diameter, etc. Look at the information line at the bottom of the screen when you select an object. Notice that the radius is rounded off to “.366” but the diameter is correctly shown as “.733” (instead of .732 which would be the case if it only used the displayed value).
Also, be aware that when you create a drawing of the object, you can specify up to four significant digits for the dimension callouts — and the system will remember what you entered.
And if you really do want to place a point at an exact location, probably the easiest way is to sketch a line starting from the origin (or perhaps a rectangle if you need “x,y coords”) and enter the exact values required. Then, make sure you turn OFF grid snapping but turn ON endpoint snapping and simply move your target object until its center “snaps” to the desired location.