The inorganic sedimentary rock with the smallest size sediments is claystone.

Here's why:

* Clay is the smallest size category of sediment, with particles less than 0.0039 mm in diameter.

* Claystone is a sedimentary rock primarily composed of clay minerals.

While other rocks like shale and mudstone can also contain clay, claystone is specifically named for its high clay content, indicating its very fine-grained nature.