Units and Units Conversion Exercises - KEY
A. What would be the results of the following calculations?
1. 36 mm2 / 12 mm = 3 mm
Convert your answer to cm: 0.3 cm
=3 x 10-1 cm
2. 120 s x 15 m/s = 1800 m
Convert your answer to feet: 5940 ft
3. 34 cm + 29 cm = 63 cm
Convert your answer to meters: 0.63 m
4. 14 cm x 5 cm x 59 cm = 4130 cm3
Convert your answer to m3: 0.00413 m3
=4.13x 10-3 m3
B. Practice the following conversion problems.
1. A facility emits 100 pounds of pollutants per day. How many pounds does it emit per
second?
100 lbs
1 day
1 day
1 hr
1 min
X
X
24 hrs
60 min
60 sec
= 0.001157 lbs/sec or 1.157 x 10-3 lbs/sec
X
=
100 lbs
86400 sec
2. The same facility emits 50 µg of PM10 per m3 in a 24-hour period. How much PM10 is
emitted per hour on average?
50 g/m3
24 hr
=
2.08 µg
(m3)(hour)
3. A volume of air sampled was 5 m3, how many liters were sampled?
5 m3
x
1.3 yd3
1 m3
x
764 L
1 yd3
= 5000 L
4. According to the Code of Federal Regulations, you must site your monitor 20 meters
away from the dripline of a tree. Could this distance be measured with a 50-foot
measuring tape?
20 m
3.3 ft
= 66 feet
1m
No, you would not be able to use a 50-ft measuring tape
x
5. If the training room is 20 x 30 feet, how many square meters is it? If the height of the
room is 11 feet, what is the volume of the room (how many cubic meters (m3) is it)?
20ft x 30ft = 600 ft2 = 55.09 m2
600 ft2
x
1m
3.3 ft
x
1m
3.3 ft
11 ft = 3.33 m
=
600 m2
10.8
= 55.6 m2 x 3.33 m = 185 m3
3/8/2016
C. Challenge Problem #1
After a 24-hour run of a PM10 MiniVol air sampler, the particulate mass on the filter weighed
0.0004 grams. If the volume of air sampled was 7170 liters, what is the concentration of PM
in the atmosphere? Convert your results to micrograms per cubic meter (µg/m3). Round your
answer to one decimal place.
0.0004 g
7170 L
400 g
7.17 m3
x
1000000 g
1g
= 400 µg
x
0.001 m3
1L
= 7.17 m3
= 55.8 µg/ m3
Challenge Problem #2
If you have a daily average of 530 g of particulate matter on a filter for a one month period,
how many kilograms (kg) of particulate matter have you collected total for that month?
Express your answer in decimals and using scientific notation; assume 1 month = 30 days.
530 g
day
X
0.000001 g
1 g
X
0.001 kg
1g
=
5.3 x 10-7 kg
day
X
30 days
=
1.59x10-5 kg
Challenge Problem #3
If 55 vehicles pass in front of the Tribal Environmental Building each day (the road is one
mile long), and each vehicle emits 0.35 g/mile of SO2. How much SO2 is emitted each day
(assume each vehicle makes the trip twice each day)?
55 (vehicles)
X
2 miles
1 day
X
0.35 g SO2
1 mile
= 38.5 g SO2/day
Revised 3/8/16