# Numerical Analysis and Computation Error Problem

If the number $\,X\,$ is rounded to $\,N\,$ decimal places, then $\,\Delta X = 1 /2 \left(10^{-N}\right)$. If $\,X = 0.51\,$ and is correct to $2$ decimal places, then $\,\Delta X = 0.005\,$ and percentage accuracy is $\,0.98\%$.

How is $\,\Delta X = 0.005\,$ derived. It is very confusing.

Using your own formula with $N=2$ you get $$\Delta X = \frac{1}{2}10^{-2} = 0.005$$ and the percentage accuracy is $$100\frac{\Delta X}{X} = 100\frac{0.005}{0.51} = 0.980392\approx 0.98\%$$