Cracks in a basement floor are a very normal part of what concrete does.

As discussed in earlier postings about cracks in concrete, since concrete expands and contracts without being very flexible, it creates expansion joints for itself in the form of cracks.

These floor cracks should be of no concern since water is not expected to come through them due to the weeping tile drainage system, which would remove the water as it develops before it comes up from under the floor.

Repairing these cracks will only provide temporary aesthetic improvement and unless you want to paint the floor, it will make little difference.

It should be mentioned that if there is expansive soil under the house, this clay rich soil can expand when it gets wet. This condition can cause small hills to develop in the floor with fairly large cracks and is an indication that the foundation drainage system or weeping tile needs attention.

Keep in mind that the basement floor is just a hard surface that has been put over the dirt and usually serves no structural or waterproofing purpose.