### Metric-English Unit ConversionProblems #1-10

Problem #1: Convert 92.33 yd3 to m3

Solution:

1) Think of 92.33 yd3 this way:

92.33 yd by 1 yd by 1 yd

2) We convert yard to meters with this:

1 yd = 0.9144 m

3) Substituting, we obtain:

(92.33 yd x 0.9144 m/yd) by 0.9144 m by 0.9144 m = 70.59 m3

4) Another way to express the conversion is this:

92.33 yd3 x (0.9144 m / yd)3

Problem #2: Convert 8.75 lb/ft3 to g/mL

Solution:

1) The first step is to change lb to g. For this, we use this conversion factor:

1 lb = 453.6 g

8.75 lb/ft3 times (453.6 g/lb) = 3969 g/ft3

2) I'm going to use cm3 rather than mL. For this, we use this conversion factor:

1 foot = 30.48 cm

3969 g/ft3 times (1 ft / 30.48 cm)3 = 0.140 g/cm3

Since 1 cm3 = 1 mL, we have 0.140 g/mL

Advice: when you need to determine mL (as in the above example), it is often much more convenient to go about determining cm3. Since 1 cm3 equals 1 mL, in determining cm3, you are determining mL.

Problem #3: Convert 6000 cm2 to in2

Solution:

Problem #4: Convert 3.55 x 10-7 miles/min to hm/day

Solution:

1) Convert denominator first:

3.55 x 10-7 miles/min x (60 min / hr) x (24 hr / day) = 5.112 x 10-4 miles/day

2) Convert miles to meters, then to hectometers:

5.112 x 10-4 miles/day x (1609.34 m / mile) x (1 hm / 100 m) = 8.23 x 10-3 hm/day

Problem #5: The men's world record for the hundred-meter (100.0 m) dash was set by Usain Bolt in 2009. His time was 9.572 seconds (official value = 9.58 s). What was his average speed in: (a) m/s; (b) km/hr; (c) ft/s; (d) miles/hr

Solution:

1) m/s:

100.0 m / 9.572 s = 10.447 m/s (to four sig figs, 10.45 m/s)

2) km/hr:

10.45 m/s x (1 km / 1000 m) x (60 s / min) x (60 min / hr) = 37.62 km/hr

3) ft/s:

10.447 m/s x (3.28084 ft/ 1 m) = 34.27493548 ft/s = 34.27 ft/s

Since one meter is larger than one foot, we assign the 1 to the meter in the conversion unit.

4) miles/hr:

34.27493548 ft/s x (1 mile / 5280 feet) x (60 s / min) x (60 min / hr) = 23.37 mi/hr

You may view video of the sprint here.

Problem #6: In America, a car's gasoline efficiency is measured in miles/gallon. In Europe, it is measured in km/L. If your car's gas mileage is 40.0 mi/gal, how many liters of gasoline would you need to buy to complete a 142 km trip? Use the following conversions: 1 km = 0.6214 mi and 1 gal = 3.7854 L

Solution: When I solved this problem, I did not clear the calculator at any point before rounding off the answer to three significant figures.

Problem #7: If 4.35 x 109 gallons of rain and snow fall on the United States daily, how many kilograms of water fall on this country each hour?

Solution:

1) Convert to gal/hr:

4.35 x 109 gal/day times (1 day / 24 hr) = 1.8125 x 108 gal/hr

2) Determine weight of the gallons per hour that fall:

1.8125 x 108 gal/hr times 8.329 lb/gal = 1509631250 lb/hr

I used the density from the table here. I used the value for 70 °F, which is equal to about 21 °C

3) Convert pounds to kilograms:

1509631250 lb/hr times (1 kg / 2.20462 lb) = 6.84758 x 108 kg

To three sig figs would be 6.85 x 108 kg

Problem #8: The density of balsa wood is 7.8 lb per cubic foot. What is the weight, in kg, of a piece of balsa wood 4.0 inch by 6.0 inch by 20.0 inch?

Solution:

1) Let us determine how many cubic inches are in our piece of balsa wood:

4.0 in x 6.0 in x 20.0 in = 480 in3

2) Determine how many cubic inches are in a cubic foot:

1 ft3 = 1 ft x 1 ft x 1 ft = 12 in x 12 in x 12 in = 1728 in3

3) How much of a cubic foot is our piece of balsa wood?

480 in3 divided by (1728 in3 / ft3) = 0.27778 ft3

4) How many pounds of balsa wood do we have?

7.8 lb / ft3 times 0.27778 ft3 = 2.166684 lb

5) Convert lb to kg:

2.166684 lb times (1 kg / 2.20462 lb) = 0.9828 kg

To two sig figs, this is 0.98 kg.

Comment: we could have converted our inch values to feet by dividing each by 12 inches / foot, to get this:

0.33333 ft x 0.5 ft x 1.666667 ft = 0.027778 ft3

then, go to step 4 above.

Problem #9: A car's engine is rated at 3.60 liters (volume in the cylinders). How many cubic inches is this? (Remember: 1 L = 1000 mL and 1 mL = 1 cm3)

Solution:

1 L = 1000 cm3 = 10 cm by 10 cm by 10 cm

1 inch = 2.54 cm

(10 cm x 1 in / 2.54 cm) by (10 cm x 1 in / 2.54 cm) by (10 cm x 1 in / 2.54 cm)

3.937 in by 3.937 in by 3.937 in = 61.0234 in3 <--- cubic inches in one liter

3.60 L x (61.0234 in3 / L) = 220. in3 (to three sig figs)

Problem #10: If zinc has a density of 446 lb/ft3 , what is the density of zinc in g/cm3?

(446 lb/ft3) (453.6 g/lb) <--- converts lb to g

(446 lb/ft3) (453.6 g/lb) (1 ft3/ (123 in3) <--- converts ft3 to in3, the unit would be g/in3 if we ended here

(446 lb/ft3) (453.6 g/lb) (1 ft3/ (123 in3) (1 in3/ 2.543 cm3)

Note the style of the conversion factors, to wit:

(1 ft3/ (123 in3)

The idea is this:

1 ft3 is a cube 12 inches on a side.

1 ft3 = 12 in x 12 in x 12 in = 123 in3

Bonus Problem: The speed of light in a vacuum is 2.998 x 108 m/s. What is the speed of light in miles/sec?

Solution:

2.998 x 108 m/s times (1 mile / 1609.34 m) = 186,288 mile/s (not paying any attention to sig figs)

Just remember what Al (our pal) Einstein said.