I've been learning how to use the power series for e^x, however I'm confused as to what level of 'accuracy' you are supposed to go to.
For instance, the question:
Determine the value of 5e^0.5, correct to 5 significant figures, by using the power series for e^x.
As I begin to multiply 0.5 by the power 2 and divide by the factorial 2, I add one to the power and factorial every time and this increases the accuracy of my answer. However there is no telling how accurate a question (like the one above) wants my answer to be. I could multiply 0.5 by the power of a billion and divide by the factorial of a billion if I wanted, theoretically I think it's infinite.
Am I missing some kind of rule here? Answering this question without knowing how accurate it needs to be seems impossible.
If someone can help me out here that would be great.