To determine how to convert the length of a shoe from inches to centimeters, we need to find the appropriate unit conversion fraction.
We know that 1 inch is equivalent to 2.54 centimeters. This information allows us to set up the correct conversion factor to convert from inches to centimeters.
To convert from inches to centimeters, you multiply the length value in inches by a conversion factor that allows inches to cancel out and leave the result in centimeters.
Among the given options:
A. [tex]\(\frac{1\text{ in}}{1\text{ cm}}\)[/tex]: This fraction suggests that 1 inch is equal to 1 centimeter, which is incorrect.
B. [tex]\(\frac{1\text{ in}}{2.54\text{ cm}}\)[/tex]: This fraction suggests dividing the length in inches by 2.54 to get centimeters, which is incorrect.
C. [tex]\(\frac{1\text{ cm}}{2.54\text{ in}}\)[/tex]: This fraction suggests that 1 centimeter is equal to 2.54 inches, which is incorrect.
D. [tex]\(\frac{2.54\text{ cm}}{1\text{ in}}\)[/tex]: This fraction correctly represents that 1 inch is equal to 2.54 centimeters.
Therefore, the correct unit conversion fraction to use is:
D. [tex]\(\frac{2.54\text{ cm}}{1\text{ in}}\)[/tex]
This conversion factor will allow us to correctly convert the length of the shoe from inches to centimeters.
