Sure, let's break down the conversion process step by step.
The goal is to convert the density of mercury from [tex]\( \text{grams per cubic centimeter (g/cm}^3 \text{)} \)[/tex] to [tex]\( \text{kilograms per cubic meter (kg/m}^3 \text{)} \)[/tex].
Given:
- The density of mercury is [tex]\( 13.6 \, \text{g/cm}^3 \)[/tex].
- [tex]\( 1 \, \text{kg} = 1,000 \, \text{g} \)[/tex].
- [tex]\( 1 \, \text{m}^3 = 10^6 \, \text{cm}^3 \)[/tex].
### Step-by-Step Conversion:
1. Convert grams to kilograms:
Since [tex]\( 1 \, \text{kg} = 1,000 \, \text{g} \)[/tex], we can rewrite [tex]\( 13.6 \, \text{g/cm}^3 \)[/tex] in kilograms as:
[tex]\[
13.6 \, \text{g/cm}^3 \times \frac{1 \, \text{kg}}{1,000 \, \text{g}}
\][/tex]
2. Convert cubic centimeters to cubic meters:
Since [tex]\( 1 \, \text{m}^3 = 10^6 \, \text{cm}^3 \)[/tex], and we want to convert the volume from cm[tex]\(^3\)[/tex] to m[tex]\(^3\)[/tex], we multiply by:
[tex]\[
\frac{10^6 \, \text{cm}^3}{1 \, \text{m}^3}
\][/tex]
3. Combine the conversions:
With the conversions above:
[tex]\[
\frac{13.6 \, \text{g}}{\text{cm}^3} \times \frac{1 \, \text{kg}}{1,000 \, \text{g}} \times \frac{10^6 \, \text{cm}^3}{1 \, \text{m}^3}
\][/tex]
4. Simplify the expression:
[tex]\[
\frac{13.6 \times 10^6 \, \text{kg}}{1,000 \, \text{m}^3}
\][/tex]
5. Perform the final calculation:
[tex]\[
13.6 \times 10^6 \, \text{kg} \times \frac{1}{1,000 \, \text{m}^3} = 13,600,000 \, \text{kg/m}^3
\][/tex]
Therefore, the density of mercury converted to [tex]\( \text{kg/m}^3 \)[/tex] is [tex]\( 13,600,000 \, \text{kg/m}^3 \)[/tex].
