[Avodah] How should we relate to numbers in Chazal?

[Marty Bluke via Avodah]

Daf Yomi is now learning the Gemara in Gittin (55-58) which deals with the
destruction of the second beis hamikdash. The Gemara uses numbers to
express the enormity of the churban, some of the numbers are completely out
of the scope of reality and others are just very large. How should we
relate to these numbers? Here are some examples.

Gittin 47 - The Gemara describes how populous the area of Har Bracha was as
follows. There were 600,000 cities, each city containing 600,000 people.
That adds up to 360 billion people, considering that the total world
population today is only about 8 billion the number cannot be taken
literally. However, the Gemara says that a Tzeduki questioned the number
and was told that the land of Israel is like a deer that it expands to meet
the population. From the Gemaras answer it seems that the 360 billion
number is to be taken at least somewhat literally and yet we all understand
that it can't be.

Gittin 47b - Nevuzarden killed 2.1 million people in a valley near
Yerushalayim and he killed 940,000 people on a rock in the Beis Hamikdash
near where Zecharia's blood was boiling. These numbers too must be
exaggerations, there is no way that Nevuzarden killed 3 million at one
time. Just remember,it took the Nazis using modern technology years to kill
6 million Jews.

Gittin 47b The Gemara has 2 opinions as to how many people were killed in
Beitar either 4 million or 40 million. The 40 million number is clearly an
exaggeration as there were nowhere near that many Jews in existence at the
time. Even the 4 million number is not realistic given population numbers
and how war was waged at that time.

So how do we relate to these numbers? Why would Chazal exaggerate the
numbers so? How do we know when Chazal are exaggerating and when they
aren't? Do any Rishonim/Acharonim take all of these numbers literally?
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