Question

other conversion factors
1.0 l = 1.057 qt
1.0 gal = 4.0 qt
1.0 lb = 16 oz
1.0 kg = 2.205 lb
1.0 in = 2.54 cm
5280 ft = 1 mi
12 in = 1 ft
1.0 ml = 1 cm³
make the following conversions using factor - label method:

1. convert 50 gallons to liters
2. convert 600 milligrams into grams
3. how many feet is 500 inches (express answer as a decimal)?
4. how many grams are in 45 ounces?
5. convert 2 liters into milliliters?
6. convert 40 cubic feet to cubic centimeters
7. how many mg/l are in a solution having 4 grams of nacl dissolved in 3 gallons.
8. if water is flowing at a rate of 8000 gallons per minute, how many cubic feet per day will flow into the reservoir.
9. if a pump is pumping at a rate of 15 gallons per minute and runs for 2 hours each day, how long will it take to fill a 20000 gallon swimming pool (convert 20000 gallons to hours).
10. calculate how many feet per second water is flowing in a grit chamber if a ball floats 250 meters in 1.43 minutes.

Explanation:

Step1: Identify conversion factors

1 gal = 3.78541 L, 1 g = 1000 mg, 1 ft = 12 in, 1 oz = 28.3495 g, 1 L = 1000 mL, 1 ft³= 28316.846592 cm³, 1 gal = 3.78541 L, 1 day = 1440 min, 1 m = 3.28084 ft, 1 min = 60 s

Step2: Solve problem 21

$50\ gal\times\frac{3.78541\ L}{1\ gal}=189.2705\ L\approx189.27\ L$

Step3: Solve problem 22

$600\ mg\times\frac{1\ g}{1000\ mg}=0.6\ g$

Step4: Solve problem 23

$500\ in\times\frac{1\ ft}{12\ in}=\frac{500}{12}\ ft\approx41.67\ ft$

Step5: Solve problem 24

$45\ oz\times\frac{28.3495\ g}{1\ oz}=1275.7275\ g\approx1275.73\ g$

Step6: Solve problem 25

$2\ L\times\frac{1000\ mL}{1\ L}=2000\ mL$

Step7: Solve problem 26

$40\ ft^{3}\times\frac{28316.846592\ cm^{3}}{1\ ft^{3}} = 1132673.86368\ cm^{3}\approx1132673.86\ cm^{3}$

Step8: Solve problem 27

First convert gallons to liters: $3\ gal\times3.78541\ L/gal = 11.35623\ L$
Then convert grams to milligrams: $4\ g\times1000\ mg/g=4000\ mg$
$\frac{4000\ mg}{11.35623\ L}\approx352.23\ mg/L$

Step9: Solve problem 28

$8000\ gal/min\times1440\ min/day\times\frac{1\ ft^{3}}{7.48052\ gal}\approx15456000\ ft^{3}/day$

Step10: Solve problem 29

The pump pumps $15\ gal/min\times120\ min/day = 1800\ gal/day$
To fill a 20000 - gallon pool, $\frac{20000\ gal}{1800\ gal/day}\approx11.11\ days$

Step11: Solve problem 30

First convert meters to feet: $250\ m\times3.28084\ ft/m = 820.21\ ft$
Then convert minutes to seconds: $1.43\ min\times60\ s/min = 85.8\ s$
$\frac{820.21\ ft}{85.8\ s}\approx9.56\ ft/s$

Answer:

1. $189.27\ L$
2. $0.6\ g$
3. $41.67\ ft$
4. $1275.73\ g$
5. $2000\ mL$
6. $1132673.86\ cm^{3}$
7. $352.23\ mg/L$
8. $15456000\ ft^{3}/day$
9. $11.11\ days$
10. $9.56\ ft/s$