Small Crack In Floor Slab
There is very little that you can do about small cracks
in a concrete floor slab. However, I would recommend that you fill these
cracks with a concrete Epoxy or caulking, before installing a new floor.
This will prevent moisture from seeping underneath your concrete floor slab, into your flooring. This will become a big problem, if you have a wood floor or carpeting.
A crack like this, looks like it could be a problem in the future, only if it gets larger. However, the only way that you will be able to check to see if this crack is getting larger, would be to remove your flooring and will usually be something difficult to do.
Cracks like these are common and I wouldn't worry about them. If the crack starts to become larger than a quarter of an inch wide, I would advise you to contact a building professional that can evaluate the situation properly.
There are a few things that could create a big problem, in your concrete foundation slab and the most common of them, would be poor soil conditions, directly underneath your home. You could also have water leaking or draining problems, with in your home or on your property, that are causing the soil to erode underneath your foundation.