Let's start by understanding the conversion. We need to convert the measurement [tex]\(0.050 \, \text{Pa} \cdot \text{cm}^3\)[/tex] into [tex]\(\text{kPa} \cdot \text{m}^3\)[/tex].
### Step-by-Step Conversion Process:
1. Convert Pascals (Pa) to Kilopascals (kPa):
- We know that [tex]\(1 \, \text{Pa} = 0.001 \, \text{kPa}\)[/tex].
2. Convert Cubic Centimeters (cm³) to Cubic Meters (m³):
- We know that [tex]\(1 \, \text{cm}^3 = 0.000001 \, \text{m}^3\)[/tex].
### Applying the Conversion Factors:
First, represent the conversions as fractions:
1. For Pressure:
[tex]\[
\frac{0.001 \, \text{kPa}}{1 \, \text{Pa}}
\][/tex]
2. For Volume:
[tex]\[
\frac{0.000001 \, \text{m}^3}{1 \, \text{cm}^3}
\][/tex]
Next, multiply these fractions by the given measurement [tex]\(0.050 \, \text{Pa} \cdot \text{cm}^3\)[/tex]:
[tex]\[
(0.050 \, \text{Pa} \cdot \text{cm}^3) \times \left( \frac{0.001 \, \text{kPa}}{1 \, \text{Pa}} \right) \times \left( \frac{0.000001 \, \text{m}^3}{1 \, \text{cm}^3} \right)
\][/tex]
We need to fill in the missing part of the equation, which are the conversion factors:
[tex]\[
\left(0.050 \, \text{Pa} \cdot \text{cm}^3\right) \cdot \left( \frac{0.001 \, \text{kPa}}{1 \, \text{Pa}} \right) \cdot \left( \frac{0.000001 \, \text{m}^3}{1 \, \text{cm}^3} \right) = 5 \times 10^{-11} \, \text{kPa} \cdot \text{m}^3
\][/tex]
So, the missing part of the equation is:
[tex]\[
\boxed{\left( \frac{0.001 \, \text{kPa}}{1 \, \text{Pa}} \right) \cdot \left( \frac{0.000001 \, \text{m}^3}{1 \, \text{cm}^3} \right)}
\][/tex]
This completes the step-by-step solution for converting the measurement.
