Why do scriptures give specific yet astronomical figures for things like the dimensions of Noah's ark and the tower of Babel? [Spirituality & Religion]

Well, I believe biblical math has pi as 3.00, and it couldn't make up it's mind as to how many horses were in Solomon's stable. Maybe it's another clue like the clue in Jeremiah 8:8.
""'How can you say, "We are wise because we have the word of the LORD," when your teachers have twisted it by writing lies?''

It's just a story, and a fun one. All of those stories in Genesis were intended for children, like fairy tales, to explain things that can't be explained.

The bible does not say how tall the tower of Babel was or even give a measurement of how tall they planned it to be. And ships have been built 3 times longer than the ark.

cause exaggerating the numbers makes things sound more impressive

Well you have to consider the audience, you'd have to throw some reference at them so they get an idea and you couldn't say "it's as big as mount whatever" cause most people probably never left their village and would be like "whaaat?" so throw in some numbers and a measurment unit that they know.

Well he had to hold all the animals the the world and they wanted to go to heaven

Is there a measurement [i]less[/i] specific than the cubit? :)