${10}^{-4} \mathrm{g}$ of gelatin is required to be added to $100{ \mathrm{cm}}^3$ of a standard gold solution to just prevent precipitation by addition of $1{ \mathrm{cm}}^3$ of $10\% \mathrm{NaCl}$ solution to it. Hence the gold number of gelatin is

Gold number is the quantity of protective colloid that is just enough to stop 10 mL of a standard hydro gold sol from coagulating when 1 mL of a 10% sodium chloride solution is added to it. 

This indicates that if the protective power is strong, the gold number will be lower, and if the protective force is weak, the gold number will be higher. 

Therefore we can say that Amount of gelatin required to protect $10 \mathrm{mL} \left(\mathrm{or} 10 {\mathrm{cm}}^3\right)$ of gold solution:

 $\mathrm{Gold} \mathrm{number}=\frac{{10}^{-4}\times 10 }{100}=$ ${10}^{-5} \mathrm{g}\times {10}^3 \mathrm{mg}={10}^{-2 }\mathrm{mg}=0.01 \mathrm{mg}$

Hence, the correct option is (D).