Comment by ndriscoll
Assuming you want to be able to make statements like ℕ⊆ℚ⊆ℝ (as one normally does), 3.0 is a whole number, 3 is a real number, and 3.0=3=2.9999999...
Being equal to 3, 2.9999... is also a whole number.
Teaching to use '=' in a statement like '10/3=3' is an example of where teachers don't know math in depth and make errors about details that are actually important/later cause confusion. 10/3 is not equal to 3. '=' doesn't mean "answer". Then not accepting 3.0 which is equal to 3 just layers on that confusion. '=' is transitive. If a=b and b=c, then a=c.
Saying 3.0≠3 is a subtlety you really only get into in math when defining these things, and then you immediately redefine them so that 3.0=3 and you don't have to think about it again.
You're continuing to focus on the functional similarities and functional equivalences of 3, 3.0, 6/2, 2.999... etc. You're right, from an arithmetic standpoint, these are all the same value. I've definitely always agreed with this and fully understand it.
But the question wasn't testing that you knew how to divide and round. The question was testing if you understood what the teacher was trying to teach about whole numbers, integers, rational numbers, real numbers, etc.
6/2 as written is not an integer. It is not a whole number. The value it represents can be written as a whole number, I fully agree, but as written it itself is not a whole number. Whole numbers are the set of numbers Z including -3, -2, -1, 0, 1, 2, 3, 4,... I doubt any math teacher, upon teaching "what is a whole number", draws a number line and proceeds to label it -3.999, -6/2, -12/6, -5/5, 0, 5/5, 12/6, 6/2, 3.999..., and on.
The notation was the key part of the question and was a key part of the answer.
The teacher wasn't looking for a value (which is what you're so focused on looking at), they were looking for a notation, a format.