Step 1 :The significant figures in a number are digits that carry meaningful information about its precision. In the given measurement, $0.0002 \mathrm{~g}$, the significant figures are the non-zero digits and any zeros between them. In this case, the number 2 is the only significant figure.
Step 2 :Final Answer: The measurement $0.0002 \mathrm{~g}$ has \(\boxed{1}\) significant figure.