The radius of a hydrogen atom is approximately \( 5.29 \times 10^{-11} \) meters. To express this in millimeters, we note that 1 millimeter is \( 10^{-3} \) meters.
Converting the radius into millimeters:
\[ 5.29 \times 10^{-11} \text{ m} = 5.29 \times 10^{-11} \times 10^{3} \text{ mm} = 5.29 \times 10^{-8} \text{ mm} \]
So the approximation of the radius of a hydrogen atom is \( 5.3 \times 10^{-8} \) millimeters (rounded to two significant figures).