marble problem

 I have a marble shower. A few of the tiles have small areas where one of the minerals in the tile  has crumbled into tiny shards. When I clean the water off the tiles with a window wiper, these tiny, minute bits have fallen out. At first, not knowing where the black bits had come from, I threw them out.

    How can I fill those small areas so that there is no more damage? I am very upset by this.

Thank you for your help.

Gale