https://file.aiquickdraw.com/mathbot/file/1730009088615h15m2342.jpg

To solve this problem, let’s analyze the setup and identify the missing component to convert from meters to centimeters.

We have:
\[
0.040 \, \frac{V}{m} \times \text{(missing factor)} = ? \, \frac{V}{cm}
\]

Here’s the step-by-step approach:

1. **Understand the Unit Conversion:** The equation is trying to convert volts per meter (\(\frac{V}{m}\)) to volts per centimeter (\(\frac{V}{cm}\)). To do this, we need a conversion factor that changes meters to centimeters.

2. **Conversion Factor:** Since \(1 \, m = 100 \, cm\), we can multiply by a factor of \(\frac{1}{100}\) to convert from meters to centimeters.

3. **Apply the Factor:** Multiplying \(0.040 \, \frac{V}{m}\) by \(\frac{1}{100}\) gives:
   \[
   0.040 \, \frac{V}{m} \times \frac{1}{100} = 0.0004 \, \frac{V}{cm}
   \]

Therefore, the missing factor is \(\frac{1}{100}\) or \(0.01\).

The completed equation would be:
\[
0.040 \, \frac{V}{m} \times 0.01 = 0.0004 \, \frac{V}{cm}
\]

Would you like further details or have questions about this?

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Here are five related questions to deepen understanding:
1. What is the general formula to convert units in physics?
2. Why is it necessary to include conversion factors in equations?
3. How would you convert \(\frac{V}{cm}\) back to \(\frac{V}{m}\)?
4. What other common conversions involve similar multiplication factors?
5. How would this equation change if we were converting from meters to millimeters?

**Tip:** Always verify the units on both sides of an equation to ensure they match; this can help identify necessary conversion factors.

A student sets up the following equation to convert a measurement. Fill in the missing part of this equation: (0.040 V/m) * [missing factor] = ? V/cm

Learn how to convert voltage measurements from volts per meter to volts per centimeter. This example covers unit conversion principles by applying a conversion factor to a measurement in physics. Suitable for students in Grades 8-10.

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