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"Convert \( \frac{1275 \text{ mm}^2}{\text{m}} \) into base units using \(1 \text{m} = 10^3 \text{ mm}\)."

To solve this, we can follow these steps:

1. The unit given is in square millimeters per meter, \( \frac{\text{mm}^2}{\text{m}} \), and we need to convert it to base SI units, which are meters.
   
2. We know \(1 \text{ m} = 10^3 \text{ mm}\), so:
   - \( 1 \text{ mm} = 10^{-3} \text{ m} \)
   - Therefore, \(1 \text{ mm}^2 = (10^{-3} \text{ m})^2 = 10^{-6} \text{ m}^2 \)

3. Now, convert \( 1275 \text{ mm}^2/\text{m} \) to base units:
   \[
   \frac{1275 \text{ mm}^2}{\text{m}} = \frac{1275 \times 10^{-6} \text{ m}^2}{\text{m}} = 1275 \times 10^{-6} \text{ m}
   \]

4. Simplifying this gives:
   \[
   1275 \times 10^{-6} \text{ m} = 1.275 \times 10^{-3} \text{ m}
   \]

Thus, the conversion of \( \frac{1275 \text{ mm}^2}{\text{m}} \) into base units is \( 1.275 \times 10^{-3} \text{ m} \).

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Would you like further details on this process or have any specific questions? Here are some related questions:

1. How does the exponent change when converting between square and linear units?
2. What is the general method for converting complex units in different systems?
3. Why do we use base SI units for such conversions?
4. How does dimensional analysis help in verifying unit conversions?
5. Can you explain how to convert cubic units to their base form?

**Tip:** When dealing with unit conversions, always ensure that both the numerical value and the units are correctly scaled using the appropriate power of 10.

Convert 1275 mm^2/m into base units using 1 m = 10^3 mm.

Learn how to convert 1275 mm²/m into base SI units using the conversion factor 1 m = 10^3 mm. This problem demonstrates unit conversion techniques, focusing on dimensional analysis and the power of 10 rules. Suitable for high school students.

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