I'm reading Sauers textbook on Numerical Methods.
An exercise where I use the Bisection method to apporoximate a root to a given function, the answer is supposed to be given with six correct decimals.
My question. If the function I use gives me an error of max $5*10^{-8}$ and my approximate root is $r_a=1.12345448000$
Disregarding the computational error of the computer, the root should be within $r= \pm 5*10^{-8}$.
It could max be $1.12345453000$ and min $1.12345443000$. Rounded these would be $1.123455$ and $1.123454$. It is not hard to imagine a smaller error (e.g. $5*10^{-14}$ but with a approximate root of $1.123454499...996$ where max approx root would be $1.123454500...001$ and min $1.123454499...991$. How do I round to the sixth decimal in this case?