To express the radius of a hydrogen atom, which is \(0.0000000529177\) of a millimeter, as an approximation, we can round it to a more manageable number.
The original number is \(0.0000000529177\).
When rounding to two significant figures, we take the first two non-zero digits which are 5 and 2. The next digit (9) tells us to round up, resulting in:
\[ 0.000000053 \]
This is written in scientific notation as \(5.3 \times 10^{-8}\) or as \(0.000000053\).
Among the options provided in your responses, the closest approximation is:
0.00000005
as it rounds down and is the nearest value represented from your available choices. However, note that's still a bit under the actual rounded value, \(0.000000053\).
If you are strictly looking for the closest approach within the listed options, the answer is 0.00000005.