To convert a measurement from [tex]\(\frac{N}{cm}\)[/tex] to [tex]\(\frac{N}{mm}\)[/tex], we need to use a conversion factor that accounts for the difference in the units of length.
Given:
[tex]\[ 0.020 \frac{N}{cm} \][/tex]
We know that:
[tex]\[ 1 \text{ cm} = 10 \text{ mm} \][/tex]
Thus, the conversion factor from cm to mm is 10. This factor represents the necessity to divide by 10 when converting from [tex]\(\frac{N}{cm}\)[/tex] to [tex]\(\frac{N}{mm}\)[/tex], because each centimeter contains 10 millimeters, meaning the numerical value has to be divided by 10 to reflect the smaller unit.
The equation would then be:
[tex]\[
\left(0.020 \frac{N}{cm}\right) \cdot \frac{1}{10} = 0.002 \frac{N}{mm}
\][/tex]
Therefore, filling in the missing part of the equation gives:
[tex]\[
\left(0.020 \frac{N}{cm}\right) \cdot 0.1 = 0.002 \frac{N}{mm}
\][/tex]
So the equation with the missing part filled in is:
[tex]\[
\left(0.020 \frac{N}{cm}\right) \cdot 0.1 = 0.002 \frac{N}{mm}
\][/tex]
