What is "find a solution accurate to within 10^-4 mean in Bisection method?

Question

If I for example after "9" iterations get the following :

p_9 = 1.365234375

and the actual p is given as:

p = 1.365230013

Is it simply saying that p_9 is within 10^-4 because the first 4 numbers 1.365 match up?

Answer 1

It likely means $$ \lvert p - p_9 \rvert < 10^{-4} $$

Answer 2

In the bisection method, you have a bracketing interval $[a_k,b_k]$ that gets bisected in every step. As the exact point and the next midpoint are both inside this interval, the condition to check is $$ |b_k-a_k|<10^{-4}, $$ as the error is guaranteed to be smaller than that.