To convert \( 2.998 \times 10^8 \) meters per second squared \((\text{m/s}^2)\) to kilometers per hour squared \((\text{km/hr}^2)\), follow these steps:

1. **Convert meters to kilometers:**
   \[
   1 \, \text{meter} = 0.001 \, \text{kilometers}
   \]
   So, \( 2.998 \times 10^8 \, \text{m/s}^2 \) becomes:
   \[
   2.998 \times 10^8 \, \times \, 0.001 \, \text{km/s}^2 = 2.998 \times 10^5 \, \text{km/s}^2
   \]

2. **Convert seconds squared to hours squared:**
   \[
   1 \, \text{second} = \frac{1}{3600} \, \text{hours}
   \]
   So, \( 1 \, \text{second}^2 = \left(\frac{1}{3600}\right)^2 \, \text{hours}^2 \):
   \[
   1 \, \text{s}^2 = \frac{1}{3600^2} \, \text{hr}^2 = \frac{1}{12960000} \, \text{hr}^2
   \]

3. **Combine the conversions:**
   Multiply \( 2.998 \times 10^5 \, \text{km/s}^2 \) by \( 1 \, \text{s}^2 \) converted to \( \text{hr}^2 \):
   \[
   2.998 \times 10^5 \, \times \, 12960000 \, \text{km/hr}^2 = 3.883008 \times 10^{12} \, \text{km/hr}^2
   \]

So, \( 2.998 \times 10^8 \, \text{m/s}^2 \) is equivalent to \( 3.883008 \times 10^{12} \, \text{km/hr}^2 \).

Would you like more details or have any questions? Here are five related questions:

1. How do you convert acceleration from m/s² to km/hr² in general?
2. What are the units of acceleration, and how do they relate to velocity and time?
3. How would you convert kilometers per hour squared back to meters per second squared?
4. Can you explain the significance of the conversion factor \(3600^2\) when converting time units?
5. How do dimensional analysis methods help ensure correct unit conversions?

**Tip:** Always check units at each step when converting to ensure accuracy!

Learn how to convert acceleration from meters per second squared (m/s²) to kilometers per hour squared (km/hr²) with a detailed step-by-step solution. This problem covers unit conversion and the application of conversion formulas for acceleration units. Suitable for advanced high school students.

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