An approximation $\overline{x}$ of $x$ is said to have $t$ correct decimals if and only if $|\overline{x}-x| \leq \frac{1}{2} 10^{-t}$.
Suppose that $\overline{x} = x \pm \frac{1}{2} 10^{-k}$ and $f(x) = \sqrt{x}$, then: $$\vartriangle f = f(\overline{x})-f(x) \approx f'(x) e_a(\overline{x},x) = \frac{1}{2\sqrt{x}} \frac{1}{2} 10^{-k}$$.
I don't know whether am I messing things up or not, some help would be appreciated.