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The equation you've uploaded involves converting between units in different measurement systems, specifically from \( \text{g} \cdot \text{cm} \) to \( \text{kg} \cdot \text{m} \). Let's break it down:

You are asked to fill in the blue box, where we need to determine the conversion factor between these two units:

1. \( \text{mol} \cdot (\text{g} \cdot \text{cm})^{-2} \) is given.
2. The goal is to express the same quantity in \( \text{mol} \cdot (\text{kg} \cdot \text{m})^{-2} \).

### Unit Conversion:

- Grams to kilograms: \( 1 \, \text{kg} = 1000 \, \text{g} \), so \( 1 \, \text{g} = 10^{-3} \, \text{kg} \).
- Centimeters to meters: \( 1 \, \text{m} = 100 \, \text{cm} \), so \( 1 \, \text{cm} = 10^{-2} \, \text{m} \).

Thus, we need to convert:
\[
\frac{1}{\text{g} \cdot \text{cm}^2} = \frac{1}{10^{-3} \, \text{kg} \cdot (10^{-2} \, \text{m})^2}
\]
\[
= \frac{1}{10^{-3} \cdot 10^{-4} \, \text{kg} \cdot \text{m}^2} = 10^7 \, \frac{1}{\text{kg} \cdot \text{m}^2}
\]

Now, multiplying by \( 1.9 \times 10^{-9} \), the final conversion factor is:
\[
1.9 \times 10^{-9} \times 10^7 = 1.9 \times 10^{-2}
\]

Thus, the value that goes in the blue box is:

\[
1.9 \times 10^{-2}
\]

Would you like more details or have any questions?

### Related Questions:
1. What other unit conversions are commonly used in physics?
2. How do you derive dimensional analysis in unit conversions?
3. What are some real-world examples where such unit conversions are applied?
4. Can you explain how to convert square and cubic units?
5. How can I understand the significance of conversion factors in physical equations?

### Tip:
Always remember to carry units throughout calculations to ensure consistency, especially in conversions.

Convert 1.9 x 10^-9 (mol / g·cm^2) to (mol / kg·m^2).

Learn how to convert 1.9 x 10^-9 mol / g·cm² to mol / kg·m² using dimensional analysis and unit conversion techniques. This problem covers key concepts in physics and math, including exponents, unit conversion between the metric system, and dimensional analysis.

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