When 62 inches is converted to meter (m) using dimensional analysis method, which conversion factors will be needed? Select ALL the conversions factors. \frac{1 in}{2.54 cm} \frac{2.54 cm}{1 in} \frac{1 m}{100 cm} \frac{100 cm}{1 m}
The Correct Answer and Explanation is:
Of the choices provided, the correct conversion factors are:
- \frac{2.54 cm}{1 in}
- \frac{1 m}{100 cm}
Explanation
Dimensional analysis is a method used to convert from one unit of measurement to another by multiplying the original value by one or more conversion factors. A conversion factor is a fraction that is equal to one because the numerator and denominator represent the same quantity, just in different units. The key to this method is to arrange the conversion factors so that the starting units cancel out, leaving only the desired final units.
The goal here is to convert 62 inches into meters. This conversion typically requires two steps: first from inches to centimeters, and then from centimeters to meters.
Step 1: Convert inches (in) to centimeters (cm)
The initial quantity is 62 inches. To cancel out the “inches” unit, the conversion factor must have “inches” in the denominator. The established relationship between inches and centimeters is 1 inch = 2.54 cm. The correct conversion factor is therefore \frac{2.54 cm}{1 in}.
Setting up the first part of the calculation looks like this:
62 in * (\frac{2.54 cm}{1 in})
In this expression, the “in” unit from “62 in” cancels with the “in” unit in the denominator of the fraction. After this step, the unit of the value is now centimeters.
Step 2: Convert centimeters (cm) to meters (m)
The current unit is centimeters, and the final desired unit is meters. To cancel out the “centimeters” unit, the next conversion factor must have “centimeters” in the denominator. The relationship between meters and centimeters is 1 m = 100 cm. The correct conversion factor for this step is \frac{1 m}{100 cm}.
Adding this to the calculation:
62 in * (\frac{2.54 cm}{1 in}) * (\frac{1 m}{100 cm})
The “cm” unit from the first conversion cancels with the “cm” unit in the denominator of the second conversion factor. The only unit that remains is “meters (m),” which is the target unit.
Therefore, both \frac{2.54 cm}{1 in} and \frac{1 m}{100 cm} are the necessary conversion factors to convert 62 inches to meters. The other two options are the reciprocals of these factors and would lead to incorrect unit cancellations.thumb_upthumb_down
