To calculate the density of the gold ring, you can use the formula for density:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
In this case, the mass of the gold ring is 15.83 grams and the volume is 0.82 milliliters. Plugging in these values:
\[ \text{Density} = \frac{15.83 , \text{grams}}{0.82 , \text{milliliters}} \approx 19.29 , \text{grams per milliliter} \]
Therefore, the density of the gold ring is approximately 19.29 grams per milliliter.