Question

1. what is the resulting unit from the calculation shown below? ( 10 \text{ km} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{100 \text{ cm}}{1 \text{ m}} \times \frac{1 \text{ in}}{2.54 \text{ cm}} \times \frac{1 \text{ ft}}{12 \text{ in}} = ? ) options: ft, in, cm, km

Explanation:

Step1: Analyze unit cancellation for km

The first conversion factor is $\frac{1000\mathrm{m}}{1\mathrm{km}}$. When we multiply $10\mathrm{km}$ by this, the $\mathrm{km}$ units cancel: $10\mathrm{km} \times \frac{1000\mathrm{m}}{1\mathrm{km}} = 10\times1000\mathrm{m}$, so unit is $\mathrm{m}$.

Step2: Analyze unit cancellation for m

Next, multiply by $\frac{100\mathrm{cm}}{1\mathrm{m}}$. The $\mathrm{m}$ units cancel: $10\times1000\mathrm{m} \times \frac{100\mathrm{cm}}{1\mathrm{m}} = 10\times1000\times100\mathrm{cm}$, unit is $\mathrm{cm}$.

Step3: Analyze unit cancellation for cm

Then, multiply by $\frac{1\mathrm{in}}{2.54\mathrm{cm}}$. The $\mathrm{cm}$ units cancel: $10\times1000\times100\mathrm{cm} \times \frac{1\mathrm{in}}{2.54\mathrm{cm}}$, unit becomes $\mathrm{in}$.

Step4: Analyze unit cancellation for in

Finally, multiply by $\frac{1\mathrm{ft}}{12\mathrm{in}}$. The $\mathrm{in}$ units cancel: The remaining unit after all cancellations is $\mathrm{ft}$.

Answer:

A. ft