You can hang up cutting mats, or store them between mattress and box spring when not in use. I have one big one that lives under an area rug until it's time to cut long strips. If you find you are repeatedly cutting in the same place, you may want to flip the mat over, or at least turn it, to even out the wear.
I don't think leaving rulers on the floor is a good idea at all - slippery, fragile, AND expensive.I have a large portfolio-type bag that holds the ones I rarely use, and my everyday ones hang from the ends of a bookcase.