What name is given to microscopic, one-celled animals typically found in decayed materials and contaminated water?

The term used to describe microscopic, one-celled animals typically found in decayed materials and contaminated water is protozoa. These organisms are classified within the kingdom Protista and are known for their diverse shapes and methods of movement, such as using pseudopodia, flagella, or cilia. Protozoa play essential roles in various ecosystems, including nutrient recycling and serving as a food source for larger organisms.

Bacteria, while also microscopic and unicellular, are distinct from protozoa in that they belong to the kingdom Monera and are prokaryotic, meaning they lack a defined nucleus. Viruses are not classified as living organisms and are much smaller than bacteria and protozoa; they require a host cell to reproduce and do not fit the description provided. Fungi, although they can also be found in decayed materials, are multicellular (except for yeast) and are classified in a different kingdom altogether.

Thus, the correct identification of one-celled organisms in this context is protozoa, specifically known for their presence in decayed materials and contaminated water.