It sounds like you understand the basic concept. The shutter speed means how long the shutter will stay open when you press the button, and like you said, it's usually measured in fractions of a second. This applies to both film and digital cameras.
The larger the number, the faster the shutter speed. So obviously 1/500 would be a much faster shutter speed and a shorter exposure time than 1/90.
I'm not sure what you mean with the other part of your question. What is it showing on your DSLR? Shutter speeds are only written in one way. It will be a fraction, or sometimes it might just give a number like 500 instead of 1/500, because it's assumed that it's a fraction of a second.
But if you use manual exposure, remember that you also have to adjust the aperture. The ISO rating, shutter speed and aperture all combine to determine the overall exposure of a picture.
The aperture (F-stop) also determines what's called the "depth of field" but if you want you can do more research about that on your own. I don't want to confuse you with too much information. Basically, it means the distance in front and behind the subject that will be in focus.