Rounding errors

For a positive integer $N,$ let $x_N$ and $y_N$ be 2 numbers randomly chosen from the uniform distribution $\big[-10^N, 10^N\big].$ Denote $x_N '$ and $y_N '$ as the values of $x_N$ and $y_N$ rounded to the nearest $5^\text{th}$ decimal places, respectively.

Find the probability that the equality below does not hold true: $\lim_{N\to\infty} (x_N ' + y_N ') = \lim_{N\to\infty} (x_N + y_N).$ If this probability can be expressed as $\frac ab,$ where $a$ and $b$ are coprime positive integers, what is the value of $a+b?$