Conversion Factors: Additional Practice (Set 1)

Convert miles to feet on top and hours to seconds on the bottom, flipping the time factor.

$\dfrac{120 \text{ mi}}{1 \text{ h}} \times \dfrac{5280 \text{ ft}}{1 \text{ mi}} \times \dfrac{1 \text{ h}}{3600 \text{ s}} = \dfrac{120 \times 5280}{3600} = 176 \text{ ft/s}$

So $120$ miles per hour is $176$ feet per second.

Convert meters to kilometers on top and seconds to hours on the bottom, flipping the second factor.

$\dfrac{8 \text{ m}}{1 \text{ s}} \times \dfrac{1 \text{ km}}{1000 \text{ m}} \times \dfrac{3600 \text{ s}}{1 \text{ h}} = \dfrac{8 \times 3600}{1000} = 28.8 \text{ km/h}$

So the runner covers $28.8$ kilometers per hour.

Square kilometers hides two lengths, so square the length factor.

$2 \text{ km}^2 \times \left(\dfrac{1000 \text{ m}}{1 \text{ km}}\right)^2 = 2 \times 1000000 = 2000000 \text{ m}^2$

So $2$ square kilometers is $2{,}000{,}000$ square meters.

One hour is $3600$ seconds, so multiply the per-second amount by those $3600$ seconds. The seconds cancel, leaving a total in gallons.

$\dfrac{50 \text{ gal}}{1 \text{ s}} \times 3600 \text{ s} = 50 \times 3600 = 180000 \text{ gal}$

So the main carries $180000$ gallons in one hour.

Only the time unit changes, so multiply by the factor that cancels seconds and installs minutes.

$\dfrac{25 \text{ m}}{1 \text{ s}} \times \dfrac{60 \text{ s}}{1 \text{ min}} = 25 \times 60 = 1500 \text{ m per minute}$

So $25$ meters per second is $1500$ meters per minute.

Square feet hides two lengths, so square the length factor.

$3 \text{ ft}^2 \times \left(\dfrac{12 \text{ in}}{1 \text{ ft}}\right)^2 = 3 \times 144 = 432 \text{ in}^2$

So $3$ square feet is $432$ square inches.

A speed of $65$ miles per hour means $65$ miles in $60$ minutes, so one minute covers $\frac{1}{60}$ of those $65$ miles. Convert that distance to feet.

$\dfrac{65 \text{ mi}}{60} \times \dfrac{5280 \text{ ft}}{1 \text{ mi}} = \dfrac{65 \times 5280}{60} = 5720 \text{ ft}$

So the car covers $5720$ feet in one minute.

Convert kilometers to meters on top and hours to seconds on the bottom, flipping the time factor.

$\dfrac{72 \text{ km}}{1 \text{ h}} \times \dfrac{1000 \text{ m}}{1 \text{ km}} \times \dfrac{1 \text{ h}}{3600 \text{ s}} = \dfrac{72000}{3600} = 20 \text{ m/s}$

So $72$ kilometers per hour is $20$ meters per second.

Square feet hides two lengths, so square the length factor.

$9 \text{ ft}^2 \times \left(\dfrac{12 \text{ in}}{1 \text{ ft}}\right)^2 = 9 \times 144 = 1296 \text{ in}^2$

So $9$ square feet is $1296$ square inches, which matches one square yard.

One minute is $60$ seconds, so multiply the per-second beats by those $60$ seconds. The seconds cancel, leaving a total beat count.

$\dfrac{50 \text{ beats}}{1 \text{ s}} \times 60 \text{ s} = 50 \times 60 = 3000 \text{ beats}$

So the hummingbird beats its wings $3000$ times in one minute.

Chain the ton-to-pound and pound-to-ounce factors so tons and pounds cancel.

$3 \text{ tons} \times \dfrac{2000 \text{ lb}}{1 \text{ ton}} \times \dfrac{16 \text{ oz}}{1 \text{ lb}} = 3 \times 2000 \times 16 = 96000 \text{ oz}$

So $3$ tons is $96000$ ounces.

Square meters hides two lengths, so square the length factor.

$2 \text{ m}^2 \times \left(\dfrac{100 \text{ cm}}{1 \text{ m}}\right)^2 = 2 \times 10000 = 20000 \text{ cm}^2$

So $2$ square meters is $20000$ square centimeters.