"The waitresses misheard the numbers, so they miscalculated."
Translation:La kelnerinoj misaŭdis la nombrojn, do ili miskalkulis.
I'd like to see how the course authors explain it in the notes. I would explain it that "numero" is a number that you can write down, such as a ticket number or page number. "Nombro" in contrast shows an amount. (A large number of people were there.) My hunch at this point is that not only should "numero" be accepted, but "nombro" is wrong here.
I have been convinced that my 'hunch" above was wrong. "The waitresses misheard the amounts and so they miscalculated." Nombro is correct. The most common place you'll see "numero" is for a house number or a phone number. An even more common meaning of "numero" is "edition" - like the edition of a magazine.
No, nombro is correct here. But yes, it is messy.
As you said, nombro is the term for numbers that signify quantity. Think cardinal numbers. It's more "mathy" than numero. You can do "math" on prices, so it is nombro.
As I understand it from other comments, numero is a number with meaning by itself. They aren't particularly "mathy". You don't add telephone numbers together, right? Think of it as a label.
Ordinal numbers are numeroj; you don't add "first" and "second" together to get "third". But you can say that "third" (numero) is "two" (nombro) behind "first" (numero). So anything sequential uses numeroj. Or at least vaguely sequential.
For example, there's the word domnumero, house number. It's a label for the house. You can't assume that you can always do "math" with house numbers; there's no assurance that 612 Main Street is 100 houses away from 512 Main Street. For example, in Japan it's common to number houses by the order they were built. Or, if you build a new house that replaces two others, then there's a gap in the sequence. (I will leave it to better speakers as to how to handle "221B Baker Street".)
At the risk of sounding like a jerk, I'm not looking for "as I understand it" kinds of answers. (By the way, I invite you to check out my profile.)
I checked a few trusted resources before commenting. If anybody knows where this is explained in the course, I'd love to see it. I'd also be interested to see examples of fluent speakers saying things like "la nombro estas ses" or "mi misauxdis la nombron." If I have more time, I might dig into this a bit more later.
Well, if you're looking for experts, you're on the wrong board...you need to go to Lernu.net to be abused properly.
Back to the subject; if you've been using Esperanto for that long and never had issue with this before, then it's got to be such a minor point that it's really not worth worrying about.
It's explained in the Tips and Notes for the Numbers skill:
NOMBRO VS NUMERO
Esperanto distinguishes between nombro and numero although both are translated as “number” in English.
Nombro is a number that signifies an amount or is used to express a mathematical relationship. For example:
la nombro de personoj
the number of people
4 estas pli granda nombro ol 3.
4 is a larger number than 3.
Numero is a number used for labelling items in a series:
la numero de la domo
the house number
la lasta numero de la gazeto
the last number [edition] of the newspaper.