APPENDIX I
"The Physical Science Tool Box of Units" Answers
Practice:
Thinking about Prefixes
1.
Mega = 106 = 1,000,000
Kilo = 103 = 1,000
Centi = 10−2 = 0.01
Milli = 10−3 = 0.001
Micro = 10−6 = 0.000001
Nano 10−9 = 0.000000001
2. 300 Mega Millions
300 Mega Millions = 300 x Mega x Million = 300 x 106 x 106 = 3 x 1014
Metric to Metric
3.
a. 5 centimeters = __________ meters
10−2 centi
5 centimeters = 5 x 10–2 m
(0.05 meters)
b. 2,000 meters = __________ kilometers
103 kilo
2,000 meters = 2 x 1000 meters = 2 x 103 meters = 2 kilometers
Ciardi, T Units Answers 1 c. 650 nanometers = __________ meters
10−9 nano
650 nanometers = 650 x 10–9 meters = 6.5 x 10–7 meters
d. 20 millimeters = __________ meters
10−3 milli
20 millimeters = 20 x 10–3 meters = 2 x 10–2 meters
(0.02 meters)
e. 20 grams = __________ kilograms
Kilo is a factor of 1000, so kilograms will be smaller than grams by a factor of 1000.
20 grams = 0.020 kilograms
Time
4. Use your knowledge of seconds minutes and hours.
a. 1 hour = __________ seconds
1 h x 60 min x 60 sec = 3,600 s
1
1h
1 min
b. 1 hour = __________ nanoseconds
1 h x 60 min x 60 sec x 1 ns = 3,600,000,000,000 ns
1
1h
1 min 10−9 sec
c. 1 day = __________ seconds
1 day x 24 hours x 3600 seconds = 86,400 s
1 hour
1
1 day
Ciardi, T Units Answers 2 5. Write your current age in years and convert this to seconds.
If you were 21 years old:
21 years x 365 days x 24 hours x 3,600 sec = 6.6226 x 108 s
1 day
1 hour
1
1 year
English to Metric & Metric to English
6. Use conversion factors to convert from one system of units to another.
a. 65 mph = __________ kph
65 mi x 1.609 km = 104.5 km/hr
1 hr
1 mi
b. 65 mph = __________ m/s
65 mi x 1609 m x 1 hr = 29 m/s
1 hr
1 mi
3600 s
c. 60 inches = __________ centimeters
60 in x 2.54 cm = 152.4 cm
1
1 in
d. 60 inches = __________ meters
60 in x 2.54 cm x 1 m = 1.52 m
1
1 in
100 cm
e. 20 m/s = __________ mph
20 m x 1 mi x 3600 sec = 44.7 mi/hr
1 sec 1609 m
1 hr
f. 20 cm = __________ inches
20 cm x
Ciardi, T 1 inch = 7.87 inches
2.54 cm
Units Answers 3 Common American Quantities
7. Write your approximate weight and convert this to Newtons.
Some Examples
150 lbs x
1N
= 667 N
1
0.2248 lbs
200 lbs x
1N
= 890 N
1
0.2248 lbs
8. Cargo ships carry many megatons of consumer products. How many pounds are in 500
Megatons of cargo? (1 ton = 2000 lbs)
500 Mega tons
500 x 106 x 2000 lbs = 1 x 1012 lbs
10. The length of an American Football field is 100 yards. How many meters are in 100 yards?
100 yards x 3 feet x 12 inches x 2.54 cm x 1 m = 91.44 meters
1 yard
1 foot
1 inch
100 cm
Measurements in 2D and 3D
11. An accent rug measures 4 feet by 6 feet. Calculate the area of the rug in square feet, and
then convert the units to square meters.
4 ft x 6 ft = 24 ft2
24 ft2 x (12 in)2 x (2.54 cm)2 x (1 m)2 = 2 m2
1
(1 ft)2
(1 in)2
(100 cm)2
12. A gift box measures 12 inches by 8 inches and is 3 inches tall. Calculate the volume, and
then change the units from inches to centimeters.
12 in x 8 in x 3 in = 288 in3
288 in3 x (2.54 cm)3 = 288 in3 x 16.38 cm3 = 4,719.47 cm3
(1 in)3
1 in3
Ciardi, T Units Answers 4