Let's begin at the beginning --- riflescopes are typically designated/identified by two or three numbers, sometimes mistaken for a mathematical equation, but not so...
For example, a scope ID as 4x20x1" indicates: "4" times magnification, i.e, the image of the target viewed through the scope will appear four times larger than if viewed with the "naked" eye. "20" indicates the diameter, in millimeters, of the objective (front, light admitting) lens. (Despite the silly American aversion to metric measurements, metric is used to describe optics, even in the USA...) The 1" designation is the outside diameter of the 'scope tube, which tells you what's required for (inside diameter) of mounting rings --- OD and ID must match!
Scope bases mount on the gun itself --- either by factory or aftermarket gunsmithing or etc., and, in turn, permit fastening the scope rings --- essentially clamps around the scope tube, to the bases. Bases are offered in various heights to accommodate mounting scopes of various tube diameters, and objective bell diameters. Ruger rifles feature integral, dovetailed, ring/base mounts --- an elegant, clever, arrangement, unfortunately not adopted by other manufacturers.
.22 Rimfire, shotgun, airgun, and similar optics intended for relatively short-range use, vs. centerfile riflescopes, are parralax adjusted to comparatively shorter ranges, such as +/- 50 yards for a .22 rimfire scope --- so, make sure you've got a rimfire scope on a rimfire rifle, or, expect problems...
Hope this helps --- if inadequate, ask again --- somebody on this forum can answer any imaginable question ...