METRIC SYSTEM: PROBLEM SET I
Convert each of the following quantities from one metric unit to another by either adjusting the
numeric portion of the value or the prefix to achieve the required form.
1.
500 kPa = ? MPa
2.
0.2 dL = 20 ? L
3.
0.7 daC = ? cC
4.
40 hJ = 4000 ? J
5.
0.25 Mhz = ? khz
6.
0.1 mmol = 100 ? mol
7.
1200 lm = 0.0012 M ?
8.
2000 µs = 0.02 ? s
9.
0.006 GW = ? kW
10.
80,000 mV = 0.08 ? V
11.
2000 pm = ? nm
12.
20 kg = 0.02 ? g
13.
3 bq = ? cbq
14.
500 Mcd = 0.0005 ? cd
15.
0.6 km/s = ? m/s
16.
200 µL = ? mL
17.
300 atm = 0.3 ? atm
18.
10,000 mg = 10 ?
19.
1300 kcal = ? Mcal
20.
190 cm = 1900 ? m
21.
2 pF = ? nF
22.
200 hN = 20 ? N
23.
3000 µWb = 3 m ?
24.
30,000 cA = ? kA
25.
38 mlx = 0.38 ? lx
ANSWERS, CHEMICAL MATH REVIEW: PROBLEM SETS
METRIC SYS: PSI
DIM. ANAL: PSI
1.
0.5 MPa
1.
19.12 g
2.
20 mL
2.
20 g/ml
3.
700 cC
3.
60 cm3
4.
4000 J
4.
4.0 g
5.
250 kHz
5.
6.0 x 1022 molecules NH3
6.
100 µmol
6.
16 g Cu
7.
0.0012 Mlm
7.
15 g
8.
0.02 ds
8.
3.4 g NH3
9.
6000 kW
9.
60. ml
10.
0.08 kV
10.
0.45 R O2
11.
2 nm
11.
120 cal
12.
0.02 Mg
12.
8.2 R
13.
300 cbq
13.
0.4 cal/gC°C
14.
0.0005 Tcd
14.
20 R
15.
600 m/s
15.
80 Kcal/mole
16.
0.2 mL
17.
0.3 katm
18.
10 g
19.
1.3 Mcal
20.
1900 mm
21.
0.002 nF
22.
20 kN
23.
3 mWb
24.
0.3 kA
25.
0.38 dlx
DIMENSIONAL ANALYSIS: PROBLEM SET I
Calculate each of the following problems using the "Factor-Label Method" or dimensional analysis.
Express your answers with the correct dimension and correct number of significant digits. If the problem
contains exponential numbers, your answer must be in the exponential form with one significant digit to
the left of the decimal point.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
DIMENSIONAL ANALYSIS: PROBLEM SET II
Perform the indicated conversions utilizing dimensional analysis (Factor-Label Method) and your
knowledge of both the metric (SI) and English systems of measurement.
1.
12 ounces = ? pounds
1 pound = 16 ounces
2.
25 Kg = ? pounds
1 quart = 32 ounces
3.
1.5 quarts = ? mL
1 yard = 3 feet
4.
9.0 furlongs = ? miles
1 yard = 36 inches
5.
1.0 bolt = ? meters
1 mile = 5280 feet
6.
460 cm = ? yards
1 foot = 12 inches
7.
10. gallons = ? liters
1 gallon = 4 quarts
8.
50 acres = ? m²
1 ton = 2000 pounds
9.
96,000 meters = ? leagues
1 hour = 60 minutes
10.
500 mg = ? grains
1 minute = 60 sec.
11.
200 mm² = ? cm²
12.
12 ft x 4.0 ft x 16 ft = ? cords
13.
8 in x 12 in = ? cm²
14.
20 cm x 10 cm x 40 cm = ? liters
15.
16.
17.
600 m x 1200 m = ? hectares
18.
19.
20.
4 in x 8 in x 5 in = ? gallon
ANSWERS, DIMENSIONAL ANALYSIS: PROBLEM SET II
1.
2.
3.
1.5 qt. x 32 oz x 29.573 ml = 1400 ml
1 qt
1 oz
4.
9.0 furlongs x 220 yards x 3 ft x 1 mile = 1.1 mile
1 furlong
1 yd
5280 ft
5.
1.0 bolt x 120 ft x 12 in x 2.54 cm = 3700 cm
1 bolt
1 foot
1 inch
6.
= 5.0 yards
460 cm x 1 inch x 1 yard
2.54 cm
36 inches
7.
10. gallons x 4 quarts x 1 liter = 38 liters
1 gallon
1.057 qt
8.
1 meter²
= 200,000 meter²
50 acres x 4820 yards² x
1 acre
1.196 yards²
9.
96,000 meters x
1 km x 1 mile x 1 league = 20 leagues
1000 m
1.609 km
3 miles
10.
500 mg x
1 gram x 15.432 grains = 8 grains
1000 mg
1 gram
11.
200 mm² x
—10 mm 
12.
12 ft x 4.0 ft x 16 ft = 768 ft³ x
13.
8 in x 12 in = 96 in² x
14.
20 cm x 10 cm x 40 cm = 8000 cm³ x 1 ml x 1 liter = 8 liters
1 cm³ 1000 ml
15.
100
16.
1 hour
x 1 minute = 90 feet
60 miles x 5280 feet x
hour
1 mile
60 minutes
60 seconds
second
17.
600 m x 1200 m = 720,000 m² x 1.196 yd² x 1 acre x 1 hectare = 72 hectares
1 meter²
4840 yd² 2.471 acres
18.
1 gram
x 1000 mg x 1 gallon x 1.057 qt = 500 mg
30 grains x
gallon
15.432 grains
1 gram
4 quarts
1 liter
liter
19.
4"x8"x5"= 160 in³ x
20.
100 ppm x 1 mg/kg x 0.4536 kg x 2000 lb x 1 gram x 1 ounce = 3 ounces
ppm
1 pound
1 ton
1000 mg
28.35 g
ton
1 cm
² = 2 cm²
1 cord = 6 cords
128 ft³
—1 inch 
2.54 cm ² = 600 cm²
1 hour
x 1 minute = 30 meters
km x 1000 m x
hour
1 km
60 minutes
60 seconds
second
—1 inch 
2.54 cm ³ x 1 ml x 1 liter x 1.057 qt x 1 gal = 0.7 gal
1 cm³ 1000 ml
1 liter
4 qt