A student sets up the following equation to convert a measurement. (The ? stands for a number the student is going to calculate.)

Fill in the missing part of this equation.

[tex]\[
\left(0.040 \frac{ v }{ m }\right) \cdot \square = ? \frac{ v }{ cm }
\][/tex]



Answer :

Certainly! Let's walk through the steps needed to convert a measurement from volts per meter (V/m) to volts per centimeter (V/cm).

1. Identify the given value:
- The value is [tex]\( 0.040 \frac{v}{m} \)[/tex].

2. Determine the conversion factor:
- We need to convert meters to centimeters. We know that 1 meter is equal to 100 centimeters.
- This means the conversion factor is 100.

3. Apply the conversion factor:
- To convert from volts per meter to volts per centimeter, we need to multiply the given value by the conversion factor.

Therefore, the detailed setup of the equation will be:
[tex]\[ \left(0.040 \frac{v}{m} \right) \cdot 100 = 4.0 \frac{v}{cm} \][/tex]

So, filling in the missing part of the equation, we get:
[tex]\[ \left(0.040 \frac{v}{m} \right) \cdot 100 = 4.0 \frac{v}{cm} \][/tex]

The equation now reads as expected, demonstrating the conversion from volts per meter to volts per centimeter correctly.