Take matrix A = \begin{bmatrix}1/3&1/4\\1/4&1/5\end{bmatrix}
I have calculated the condition number of A to be 245/3 (using l1-norm)
This means we may lose about 2 significant figures of accuracy (by the rule of thumb that for a condition number K(A) you lose log(K(A)) significant figures in accuracy).
Am I right to say this means the matrix is ill-conditioned because some of the values in the matrix are only to 2sf (e.g 0.25 and 0.2) or not because these values are actually to an infinite precision as they are fractions?