How do we find the decimal (or base) expansion of a real number upto first n digits, given a sequence that converges to it?

Suppose we have a sequence ${x_n}$ that converges to some limit, say $\pi$. How do we compute out the decimal expansion of $\pi$ from that sequence? How could the epsilon definition help us here? What are some considerations to have the decimal expansion of the number is not unique?

On existence and Uniqueness of decimal expansion