### Tutorial 1.6: Part 2

Dimensional analysis: English-Metric Conversions

How do we calculate the number of cm in 4.25 yards?

If you need to get your bearings, start with the unit given, yards, and write out conversion factors (as units) until you arrive at the desired unit - the centimeter.

$yards \times \frac{feet}{ yards} \times \frac{inches}{feet} \times \frac{cm}{inches}$

Complete with numerical conversion factors.

\begin{align*} & 4.25\, yards \times \frac{3\, feet}{ yard} \times \frac{12\, inches}{feet} \times \frac{2.54 \, cm}{in} \\ & = 388.62\, cm \\ & = 389 \, cm \end{align*}

How do we calculate the number of miles equivalent to 345 hm?

If you need to get your bearings, start with the unit given, hm, and write out conversion factors (as units) until you arrive at the desired unit - miles.

$hm \times \frac{cm}{hm} \times \frac{inches}{cm} \times \frac{feet}{inches} \times \frac{mile}{feet}$

Complete with numerical conversion factors.

\begin{align*} & 345\, hm \times \frac{10^4 \,cm}{1 \,hm} \times \frac{1 \,in}{2.54 \,cm} \times \frac{1 \,foot}{12 \,inches} \times \frac{1 \,mile}{5280 \,feet}\\ & = 21.4373\, miles \\ & =21.4\, miles \end{align*}