To find the density of the platinum nugget, we use the formula for density:
[tex]\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \][/tex]
Given:
- Mass ([tex]\(m\)[/tex]) = 210.0 grams
- Volume ([tex]\(V\)[/tex]) = 9.77 cubic centimeters ([tex]\( \text{cm}^3 \)[/tex])
Plug the given values into the formula:
[tex]\[ \text{Density} = \frac{210.0 \, \text{g}}{9.77 \, \text{cm}^3} \][/tex]
By performing this division, we obtain:
[tex]\[ \text{Density} = 21.494370522006143 \, \text{g/cm}^3 \][/tex]
To express the density to three significant figures, we round the result appropriately:
[tex]\[ \text{Density} \approx 21.494 \, \text{g/cm}^3 \][/tex]
Therefore, the density of the platinum nugget is [tex]\( 21.494 \, \text{g/cm}^3 \)[/tex], expressed to three significant figures and with the appropriate units.
