Conversion Factors: Practice

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

$3 \text{ days} \times \dfrac{24 \text{ h}}{1 \text{ day}} \times \dfrac{60 \text{ min}}{1 \text{ h}} = 3 \times 24 \times 60 = 4320 \text{ min}$

So $3$ days is $4320$ minutes. The value $1440$ is the minutes in a single day.

One minute is $60$ seconds, so multiply the per-second distance by those $60$ seconds. The seconds cancel, leaving a total in meters.

$\dfrac{30 \text{ m}}{1 \text{ s}} \times 60 \text{ s} = 30 \times 60 = 1800 \text{ m}$

So the car travels $1800$ meters in one minute.

Chain the meter-to-centimeter factor and the centimeter-to-millimeter factor.

$2 \text{ m} \times \dfrac{100 \text{ cm}}{1 \text{ m}} \times \dfrac{10 \text{ mm}}{1 \text{ cm}} = 2 \times 100 \times 10 = 2000 \text{ mm}$

So $2$ meters is $2000$ millimeters. Stopping at $200$ leaves you in centimeters.

One hour is $60$ minutes, so multiply the per-minute count by those $60$ minutes. The minutes cancel, leaving a total number of pages.

$\dfrac{12 \text{ pages}}{1 \text{ min}} \times 60 \text{ min} = 12 \times 60 = 720 \text{ pages}$

So the printer prints $720$ pages in one hour.

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

$1 \text{ day} \times \dfrac{24 \text{ h}}{1 \text{ day}} \times \dfrac{3600 \text{ s}}{1 \text{ h}} = 24 \times 3600 = 86400 \text{ s}$

So one day is $86400$ seconds.

One hour is $60$ minutes, so multiply the per-minute amount by those $60$ minutes. The minutes cancel, leaving a total in liters.

$\dfrac{4 \text{ L}}{1 \text{ min}} \times 60 \text{ min} = 4 \times 60 = 240 \text{ L}$

So the faucet delivers $240$ liters in one hour.

One hour is $60$ minutes, so multiply the per-minute amount by those $60$ minutes. The minutes cancel, leaving a total in gallons.

$\dfrac{5 \text{ gal}}{1 \text{ min}} \times 60 \text{ min} = 5 \times 60 = 300 \text{ gal}$

So the pump moves $300$ gallons in one hour.

Chain the gallon-to-quart factor and the quart-to-pint factor so that gallons and quarts cancel.

$2 \text{ gal} \times \dfrac{4 \text{ qt}}{1 \text{ gal}} \times \dfrac{2 \text{ pt}}{1 \text{ qt}} = 2 \times 4 \times 2 = 16 \text{ pt}$

So $2$ gallons is $16$ pints.

Chain the kilogram-to-gram factor and the gram-to-milligram factor.

$3 \text{ kg} \times \dfrac{1000 \text{ g}}{1 \text{ kg}} \times \dfrac{1000 \text{ mg}}{1 \text{ g}} = 3 \times 1000 \times 1000 = 3000000 \text{ mg}$

So $3$ kilograms is $3{,}000{,}000$ milligrams.

Convert liters to milliliters on top and hours to minutes on the bottom. The hours factor is flipped so hours cancels.

$\dfrac{3 \text{ L}}{1 \text{ h}} \times \dfrac{1000 \text{ mL}}{1 \text{ L}} \times \dfrac{1 \text{ h}}{60 \text{ min}} = \dfrac{3000}{60} = 50 \text{ mL per minute}$

So the car uses $50$ milliliters per minute.

Chain the week-to-day factor and the day-to-hour factor so that weeks and days cancel.

$2 \text{ weeks} \times \dfrac{7 \text{ days}}{1 \text{ week}} \times \dfrac{24 \text{ h}}{1 \text{ day}} = 2 \times 7 \times 24 = 336 \text{ h}$

So $2$ weeks is $336$ hours. The value $168$ is the hours in a single week.

Multiply the rate by the factor that cancels seconds and installs minutes.

$\dfrac{2 \text{ gal}}{5 \text{ s}} \times \dfrac{60 \text{ s}}{1 \text{ min}} = \dfrac{2 \times 60}{5} = 24 \text{ gal per minute}$

So the tap fills $24$ gallons per minute.