I don't understand this claim on the bottom of page 1 (emphasis added): > It is easy to verify that with n = 1000, the error on π is of the order of 0.293193 x

I don't understand this claim on the bottom of page 1 (emphasis added): > It is easy to verify that with n = 1000, the error on π is of the order of 0.293193 x 10^-303, which is less than 2^-1000. So the thousandth position of this expression is the 1000th bit of the number π. How does that follow? Take the number 1 - 2^-n. The difference between this number and 1 is 2^-n by definition, so it can be made arbitrarily small by varying n, but all bits are wrong. Addition can propagate all the way to the "decimal" point (and even beyond), so an error bound doesn't normally say anything about individual bits or digits. What am I missing here?