M: In Google Docs, I'm trying to create a function that has the possibility of throwing a divide-by-zero problem. What's the name of a function that can handle that? So that if one of the divisors ends up being zero, it'll just give zero as the result.

G: TL;DR: Use IFERROR() (or IF() with a zero check).

In Google Sheets (the spreadsheet part of Google Docs), division by zero throws a #DIV/0! error. The standard way to neutralize that is:

Preferred, simple

=IFERROR(A1 / B1, 0)

If B1 is zero (or blank, or anything that errors), the result is 0.

More explicit / narrower

If you want to only guard against zero (not other errors):

=IF(B1 = 0, 0, A1 / B1)

Why IFERROR

Edge note

If blanks should behave differently:

=IF(B1 = "", 0, A1 / B1)

Name you were looking for: IFERROR
That’s the canonical answer.