Marble surfaces, such as floors, are susceptible to scratching from anything that's harder than the marble, which can include various types of metals, stone or grit from sand. If the scratches are more like gouges, with an actual depth into the face of the marble, you'll need to call a professional. But if they're just surface scratches, you can buff them out yourself. Does this Spark an idea?
Clean the Scratches
Scratches in marble are often caused by fine pieces of dirt or grit. Make sure the surface is clean before repairing the scratches so that more of them don't develop. Clean the entire floor with your usual tile floor cleaner. Then take a soft cloth, wet it with warm water and a little dish soap and clean the scratched areas with it. Rinse the area well to get rid of the soap.
Sand Out the Scratches
Take some cloth-backed 220-grit sandpaper, wet it thoroughly in warm water and gently rub at the scratches with it. Press lightly and rub in a short, quick motions, frequently rewetting the sandpaper. You should see the scratches start to disappear before your eyes. Continue until you've taken out all the scratches. Re-clean the whole floor thoroughly to get rid of any loose grit from the sanding.
Buff the Surface
Look at the marble from a few angles. If the areas where you rubbed out the scratches have a different sheen than the surrounding areas, then you need to re-buff the parts you sanded to get them to match the surrounding marble. Buy several kinds of very fine cloth sandpaper of increasing grit counts: 400, 600 and 800. Start with the 400-grit paper, wetting it as before and buffing at the areas. Dry the area and check the sheen against the surrounding areas. If it's still not a match, continue with the 600-grit and 800-grit paper until it is.
Tags: grit from, surrounding areas, warm water
