Changing input values under "transform" section of Details menu to "local" from world?

When moving objects like a camera around my scene, I know how to change the orientation from “world” to “local”. However, when I try to input finer, very minute changes into the “transform” section of the details menu for my object while the object’s in local, it stills calculates for world. Is there a way to change this? Even when I change the transform settings in the details menu to “relative” from “world” (fwiw, I tested it from both settings) when I input values here it still calculates them for World.

In general, I’m trying to learn an easy, convenient way to make very small, detailed movements of my objects (For example, setting a camera to shoot something close-up at JUST the right angle).

Thanks in advance.