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]\[ \left(0.020 \frac{N}{cm}\right) \cdot \square = ? \frac{N}{mm} \][/tex]



Answer :

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]