When $\frac{5}{6}$ of a bottle was filled with apple juice, its total mass was $4.6\text{kg}$. When $\frac{2}{3}$ of the bottle was filled with apple juice, its total mass was $4.45\text{kg}$. What was the mass of the empty bottle (in grams)?~\uline{~~~~~~~~~~}~ 
Overseas Competition->Knowledge Point->Calculation Modules