A limestone that contains fossils would be classified as a biogenic sedimentary rock.

Here's why:

* Biogenic means "originating from living organisms."

* Limestone is primarily composed of calcium carbonate (CaCO3), which is often formed from the skeletal remains of marine organisms like corals, shellfish, and algae.

* The presence of fossils directly indicates that the limestone was formed from the accumulation and cementation of these organic remains.

While limestone can also be classified as a chemical sedimentary rock (due to the precipitation of calcium carbonate from solution), the presence of fossils makes it primarily a biogenic rock.