To solve this equation, we need to find the appropriate factor that allows us to convert the units of the denominator from meters (m) to centimeters (cm). Here's a step-by-step explanation:
1. Understand the Units Conversion:
We know that 1 meter (m) is equal to 100 centimeters (cm). Therefore, the relationship between meters and centimeters can be written as:
[tex]\[
1 m = 100 cm
\][/tex]
2. Rewrite the Original Equation with Unit Changes:
Given the term:
[tex]\[
\left( -5.1 \times 10^3 \frac{v}{m} \right)
\][/tex]
we need to fill in the square ([tex]\(\square\)[/tex]) such that the right-hand side has the units of [tex]\(\frac{v}{cm}\)[/tex].
3. Determine the Conversion Factor:
To convert from meters (m) to centimeters (cm), we need to introduce a factor that accounts for this change. Since:
[tex]\[
1 m = 100 cm
\][/tex]
we can multiply by the factor [tex]\(\frac{1}{100}\)[/tex] to change meters to centimeters.
4. Apply the Conversion Factor:
The missing part of the equation should be the factor [tex]\(\frac{1}{100}\)[/tex], which is 0.01. This factor allows the units in the denominator to change from meters to centimeters.
5. Fill in the Equation:
Therefore, the completed equation is:
[tex]\[
\left( -5.1 \times 10^3 \frac{v}{m} \right) \cdot 0.01 = -51 \frac{v}{cm}
\][/tex]
So, the value that fills in the missing part of the equation [tex]\(\left(-5.1 \times 10^3 \frac{ v }{ m }\right) \cdot \square=? \frac{ v }{ cm }\)[/tex] is:
[tex]\(\square = 0.01\)[/tex]
