Q18P - Chemistry: Molecular Nature Of Matter And Change

Question

When you convert feet to inches, how do you decide which portion of the conversion factor should be in the numerator and which in the denominator?

Step-by-Step Solution

Answer

In the conversion factor, the numerator should have the higher value while the denominator should have the lower value because a foot is larger than an inch.

Step 1: Decide if the answer should be stated in final units with a higher or lower value

In this problem, we need to convert the physical length (distance) from feet to inches. A foot is larger than an inch, as we all know. So, the length in inches should have a higher value $\left(12\right)$ than the length in feet $\left(1\right)$. Therefore, the answer stated in the final units must have a higher value. 

Step 2: Determine the numerator and the denominator of the conversion factor

Conversion factors are fractions that are used to express a quantity in several units.

The final answer's units (inches) should be in the numerator of the conversion factor. 

The unit conversion equation that describes the conversion between feet and inches can be written as follows:

$\mathbf{\text{1 ft = 12 \hspace{0.17em}inch}}$

The unit conversion factors for converting the length between feet and inches are written below:

$\frac{\mathbf{\text{1 ft}}}{\mathbf{\text{12 \hspace{0.17em}inch}}}\mathbf{\text{ or }}\frac{\mathbf{\text{12 \hspace{0.17em}inch}}}{\mathbf{\text{1 ft}}}$

The second conversion factor has the higher value (12) in the numerator so that it makes a higher value in the final answer. This factor also cancels all ft units and leaves only inch units in the answer. Hence, the numerator and the denominator of the conversion factor are 12 inch and $\text{1\hspace{0.17em}\hspace{0.17em}ft}$ respectively.