To express the radius of a hydrogen atom, which is \(0.0000000529177\) millimeters, as an approximation, we can round it to a reasonable number of significant figures.
Looking at the number:
- The first significant figure is 5, and we can look at the digit after it (2) to determine how to round it.
- Since 2 is less than 5, we won't round up.
Thus, the approximation can be rounded to \(0.00000005\) millimeters.
So, the best choice from the given options is:
0.00000005.