How do you classify organisms as eukaryotes?

Answer: Eukaryotic cells contain membrane-bound organelles, such as the nucleus, while prokaryotic cells do not

Explanation: so if cells contain membrane-bound organelles in the organism then their classified as eukaryotes

A eukaryote is an organism with complex cells, or a single cell with a complex structures. In these cells the genetic material is organized into chromosomes in the cell nucleus. Animals, plants, algae and fungi are all eukaryotes. There are also eukaryotes amongst single-celled protists.