What exactly constitutes as an exact value?

[Permanence]

I'm not sure if this is the correct section to post in, but since it relates to calculus and this is more of a general concept than a single problem I figured here would be fine.

On a recent exam we were given a region bounded by a simple curve generated from a function that was bounded from the y-axis to a constant. We were asked to find the exact perimeter of the region. Solving the problem involved solving for the curve and the other two linear sides. Now for the curve I understand you do the integral of the square root of the derivative plus one. I did that, but when I evaluated on the calculator it came out to a very long irrational number. I felt that including a certain number of decimals would be an approximation, not an exact number. So I left it as the value of the other two sides plus the integral. The answer they wanted was anything with at least three decimals. I was not given points as my teacher felt that I did not properly evaluate the problem. Who is the right here?
Sorry if I'm being vague. We are asked not to post the problems/solutions so I was doing my best to be clear without actually giving the problem.

 

[mathman]

My guess: there is a closed form expression (what you put into the calcuator) and that is what was asked for.

 

[HallsofIvy]

If you were give $x^2+ y^2= 4$ and asked to find the circumference, "$4\pi$ would be an "exact" answer. "12.566370614359172953850573533118" would not be.

 

[Permanence]

Okay, thank you to both of you. The answer could not be written out, so I still think I was correct in the notation I used. That being said, I don't make the decisions so I'll just have to live with things.