Conversion Factors: Practice

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

$\dfrac{60 \text{ mi}}{1 \text{ h}} \times \dfrac{5280 \text{ ft}}{1 \text{ mi}} \times \dfrac{1 \text{ h}}{3600 \text{ s}} = \dfrac{60 \times 5280}{3600} = 88 \text{ ft/s}$

So $60$ miles per hour is $88$ feet per second.

Cubic feet hides three lengths, so cube the length factor.

$2 \text{ ft}^3 \times \left(\dfrac{12 \text{ in}}{1 \text{ ft}}\right)^3 = 2 \times 1728 = 3456 \text{ in}^3$

So $2$ cubic feet is $3456$ cubic inches. The value $1728$ is a single cubic foot.

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

$\dfrac{90 \text{ km}}{1 \text{ h}} \times \dfrac{1000 \text{ m}}{1 \text{ km}} \times \dfrac{1 \text{ h}}{3600 \text{ s}} = \dfrac{90000}{3600} = 25 \text{ m/s}$

So $90$ kilometers per hour is $25$ meters per second.

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

$2 \text{ yd}^2 \times \left(\dfrac{3 \text{ ft}}{1 \text{ yd}}\right)^2 = 2 \times 9 = 18 \text{ ft}^2$

So $2$ square yards is $18$ square feet.

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

$\dfrac{44 \text{ ft}}{1 \text{ s}} \times \dfrac{1 \text{ mi}}{5280 \text{ ft}} \times \dfrac{3600 \text{ s}}{1 \text{ h}} = \dfrac{44 \times 3600}{5280} = 30 \text{ mph}$

So $44$ feet per second is $30$ miles per hour.

Chain the day-to-hour and hour-to-minute factors so days and hours cancel.

$365 \text{ days} \times \dfrac{24 \text{ h}}{1 \text{ day}} \times \dfrac{60 \text{ min}}{1 \text{ h}} = 365 \times 24 \times 60 = 525600 \text{ min}$

So a $365$-day year has $525{,}600$ minutes. The value $8760$ is the number of hours.

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

$\dfrac{30 \text{ m}}{1 \text{ s}} \times \dfrac{1 \text{ km}}{1000 \text{ m}} \times \dfrac{3600 \text{ s}}{1 \text{ h}} = \dfrac{30 \times 3600}{1000} = 108 \text{ km/h}$

So the cheetah runs $108$ kilometers per hour.

Cubic yards hides three lengths, so cube the length factor.

$2 \text{ yd}^3 \times \left(\dfrac{3 \text{ ft}}{1 \text{ yd}}\right)^3 = 2 \times 27 = 54 \text{ ft}^3$

So $2$ cubic yards is $54$ cubic feet. A single cubic yard is $27$ cubic feet.

A speed of $50$ miles per hour means $50$ miles in $60$ minutes, so one minute covers $\frac{1}{60}$ of those $50$ miles. Convert that distance to feet.

$\dfrac{50 \text{ mi}}{60} \times \dfrac{5280 \text{ ft}}{1 \text{ mi}} = \dfrac{50 \times 5280}{60} = 4400 \text{ ft}$

So the car travels $4400$ feet in one minute.

Chain the day-to-hour and hour-to-second factors so days and hours cancel.

$365 \text{ days} \times \dfrac{24 \text{ h}}{1 \text{ day}} \times \dfrac{3600 \text{ s}}{1 \text{ h}} = 365 \times 24 \times 3600 = 31536000 \text{ s}$

So a $365$-day year has $31{,}536{,}000$ seconds.

Convert liters to milliliters on top and hours to minutes on the bottom, flipping the time factor.

$\dfrac{6 \text{ L}}{1 \text{ h}} \times \dfrac{1000 \text{ mL}}{1 \text{ L}} \times \dfrac{1 \text{ h}}{60 \text{ min}} = \dfrac{6000}{60} = 100 \text{ mL per minute}$

So the tank leaks $100$ milliliters per minute.

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

$1 \text{ yd}^2 \times \left(\dfrac{36 \text{ in}}{1 \text{ yd}}\right)^2 = 1 \times 1296 = 1296 \text{ in}^2$

So $1$ square yard is $1296$ square inches.