The density of gold is `19.32 g//cm^3`. Calculate its density in SI units.

Answer

To convert the density of gold from grams per cubic centimeter (g/cm³) to kilograms per cubic meter (kg/m³), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Density**:
The density of gold is given as \( 19.32 \, \text{g/cm}^3 \).

2. **Convert Grams to Kilograms**:
We know that:
\[ 1 \, \text{kg} = 1000 \, \text{g} \quad \Rightarrow \quad 1 \, \text{g} = 10^{-3} \, \text{kg} \]
Therefore, we can convert grams to kilograms:
\[ 19.32 \, \text{g} = 19.32 \times 10^{-3} \, \text{kg} \]

3. **Convert Cubic Centimeters to Cubic Meters**:
We know that:
\[ 1 \, \text{m} = 100 \, \text{cm} \quad \Rightarrow \quad 1 \, \text{cm} = 10^{-2} \, \text{m} \]
Therefore, for volume:
\[ 1 \, \text{cm}^3 = (10^{-2} \, \text{m})^3 = 10^{-6} \, \text{m}^3 \]

4. **Combine the Conversions**:
Now we can substitute these conversions into the density formula:
\[ \text{Density in kg/m}^3 = \frac{19.32 \times 10^{-3} \, \text{kg}}{10^{-6} \, \text{m}^3} \]

5. **Calculate the Density**:
Simplifying the expression:
\[ \text{Density in kg/m}^3 = 19.32 \times 10^{-3} \times 10^{6} \, \text{kg/m}^3 = 19.32 \times 10^{3} \, \text{kg/m}^3 = 19320 \, \text{kg/m}^3 \]

6. **Final Result**:
Therefore, the density of gold in SI units is:
\[ \text{Density of gold} = 19320 \, \text{kg/m}^3 \]