which era of geologic time was the longest
In the formal geological time scale, there are ten eras (the Hadean Eon isn't subdivided into eras). These are Eoarchaen, Paleoarchaen, Mesoarchaen, Neoarchaen, Paleoproterozoic, Mesoproterozoic, Neoproterozoic, Paleozoic, Mesozoic, and Cenozoic (which is the current era). The longest would be the Paleoproterozoic Era, which spanned 900 million years. If you count the Precambrian Era (which isn't an era, technically...it is a supereon), then that would be longest, spanning 3958 million years. I would go with Paleoproterozoic Era. That's an official era, whereas Precambrian is just mistakenly called an era when it is actually a much longer span of time.