To convert from dollars per foot (dollars/ft) to dollars per meter (dollars/m), let's go through the conversion factors step by step.
1. Understand the given information:
- We start with dollars per foot, which we'll denote as dollars/ft.
2. Convert feet to centimeters:
- We know there are 30.48 centimeters in one foot. Thus, the conversion factor from feet to centimeters is [tex]\( \frac{1 \, \text{ft}}{30.48 \, \text{cm}} \)[/tex].
3. Apply the conversion factor:
- To convert the dollars per foot to dollars per centimeter, we multiply dollars per foot by the conversion factor [tex]\(\frac{1 \, \text{ft}}{30.48 \, \text{cm}}\)[/tex]. This gives us:
[tex]\[
\left(\frac{\text{dollars}}{\text{ft}}\right) \cdot \left(\frac{1 \, \text{ft}}{30.48 \, \text{cm}}\right) = \frac{\text{dollars}}{30.48 \, \text{cm}} \approx 0.03280839895013123 \, \frac{\text{dollars}}{\text{cm}}
\][/tex]
4. Convert centimeters to meters:
- There are 100 centimeters in one meter. Therefore, the conversion factor from centimeters to meters is [tex]\( \frac{100 \, \text{cm}}{1 \, \text{m}} \)[/tex].
5. Apply the conversion factor:
- To convert the dollars per centimeter to dollars per meter, we multiply dollars per centimeter by the conversion factor [tex]\( 100 \, \text{cm} \)[/tex] to [tex]\( 1 \, \text{m} \)[/tex]. This gives us:
[tex]\[
\left(0.03280839895013123 \, \frac{\text{dollars}}{\text{cm}}\right) \cdot \left(100 \, \frac{\text{cm}}{\text{m}}\right) = 3.2808398950131235 \, \frac{\text{dollars}}{\text{m}}
\][/tex]
Therefore, the conversion steps show that:
- Dollars per foot converted to dollars per centimeter is [tex]\( \approx 0.03280839895013123 \, \frac{\text{dollars}}{\text{cm}} \)[/tex].
- Dollars per foot converted to dollars per meter is [tex]\( \approx 3.2808398950131235 \, \frac{\text{dollars}}{\text{m}} \)[/tex].
These are the final conversion results.
