How many zeros?

This is our first week back in school during which our students have been learning aspects of their new handheld¬† (TI-Nspire CAS) and online (Wolfram Alpha) CAS in the context of enhancing their problem-solving ideas.¬† While exploring the capabilities of these amazing computational tools, one student entered a number like 300! (That’s factorial) and was pretty impressed to see all of the digits listed.¬† Before going further, I asked

  1. how they might determine the number of digits in 300!,
  2. what the final digit was, and
  3. how many of that final digit were in an uninterrupted sequence at the end of an expanded representation of 300!.

We’ll give a few days for your ideas before posting our students’ thoughts.

Solutions are here.