Dimensional Analysis Practice Problems
Complete the dimensional analysis problems below. The first 5 of the conversions partially set up for you; fill in the blank with the correct numerical values.
1.
0.56kg = ? mg
6. 3 wk = ? min
0.56 kg x ___103____ g x __103_____ mg = 5.6 x 105 mg OR 560,000mg
3 wk x _7 days_ x __24 hr_ x __60 min_ = 30,000 minOR 3 x 104 min 1 sig fig
1 kg
1g
2 sig figs
1 wk
1 day
1 hr
2.
1.2ng = ? g
7.
50mL = ? cups (1L = 4.226cups)
1.2 ng x _____1___g =1.2 x 10-9 g 2 sig figs
50mL x __1 L__ x __4.226 cups___ = 0.2 cups OR 2 x 10-1 cups 1 sig fig
109 ng
103 mL
1L
3.
2.0 in = ? mm (1in = 2.54 cm)
8. 5.33km = ? dm
2.0 in x ___2.54__cm x ____1___ m x ___103____ mm = 25 mm 2 sig figs
5.33 km x __103 m__ x __102 dm__ = 5.33 x 105 dm 3 sig figs
1 in
102 cm
1m
1 km
1m
4. 500ft = ? m
9. 123.0 ng = ? Mg
500 ft x __12_ in x __2.54_ cm x ___1__ m = 152.4 m 200 m 1 sig fig!
123.0 ng x ___1 g__ x __1 Mg__ = 123.0 x 10-15 Mg 4 sig figs
1 ft
1 in
102 cm
109 ng
106 g
5.
10μL = ? cc (1mL = 1cm3 = 1 cc)
10. 3yds = ? in (1 yd = 3ft)
10μL x ___1__L x __103_ mL x _1_ cc = 10-2 cc OR 0.01 cc 1 sig fig
3 yds x ___________ x _____________ = ______________ in
106 μL
1 L
1 mL
REMEMBER: THE PROBLEMS ARE EASY ONCE YOU FIGURE OUT WHAT INFORMATION TO START WITH.
11. When one gram of gasoline burns in a car's engine, the amount of energy given off is approximately 1.03 x 104
cal. Express this quantity in joules (J). (Use 1 cal = 4.184 J)
12. The pressure reading from a barometer is 742 mm Hg. Express this reading in kilopascals, kPa. (Use 760 mm Hg
= 1.013 x 105 Pa)
13. How many Megayears is equivalent to 6.02 × 1023 nanoseconds (ns)?
14. The average student is in class 330 min/day.
a. How many hours/day is the average student in class? You should know what conversion factors you will need!
b. How many seconds is the average student in class per week?
c. Calculate how many seconds you are in class a day (pick any weekday you have class). Show any
calculations you have to do as dimensional analysis. Answers will vary between you and your classmates.
15. Approximately how many pounds do you weigh? ___________ lbs.
16. A child is entered into the hospital after ingesting 12 aspirin tablets. The Merck Index indicates that renal
(kidney) failure can occur if as little as 3 grams is ingested, and may be fatal if as much as 10 grams is eaten. If
each aspirin tablet contains 300 mg of aspirin, how much aspirin (in grams) has the child ingested?
Dimensional Analysis Practice Problems
Complete the dimensional analysis problems below. The first 5 of the conversions partially set up for you; fill in the blank with the correct numerical values.
1.
0.56kg = ? mg
10μL x _________L x _______ mL x ________ cc = _________ cc
0.56 kg x _______ g x _______ mg = __________ mg
μL
L
mL
kg
g
6. 3 wk = ? min
2.
1.2ng = ? g
3 wk x ___________ x _________ x __________ = _________min
1.2 ng x ________g = ___________ g
7.
50mL = ? cups
ng
50 mL x _________ x _____________ = __________ cups
3.
2.0 in = ? mm (1in = 2.54 cm)
(1L = 4.226cups)
2.0 in x _______cm x _______ m x _______ mm = ________ mm
8. 5.33km = ? dm
in
cm
m
5.33 km x ____________ x _______________ = ___________ dm
4. 500ft = ? m
9. 123.0 ng = ? Mg
500 ft x _______ in x _________ cm x _________ m = ________m
123.0 ng x _____________ x ______________ = ____________ Mg
ft
in
cm
10. 3yds = ? in (1 yd = 3ft)
5.
10μL = ? cc (1mL = 1cm3 = 1 cc)
3 yds x ___________ x _____________ = ______________ in
REMEMBER: THE PROBLEMS ARE EASY ONCE YOU FIGURE OUT WHAT INFORMATION TO START WITH.
11. When one gram of gasoline burns in a car's engine, the amount of energy given off is approximately 1.03 x
104 cal. Express this quantity in joules (J). (Use 1 cal = 4.184 J)
12. The pressure reading from a barometer is 742 mm Hg. Express this reading in kilopascals, kPa. (Use 760
mm Hg = 1.013 x 105 Pa)
13. How many Megayears is equivalent to 6.02 × 1023 nanoseconds (ns)?
14. The average student is in class 330 min/day.
a. How many hours/day is the average student in class? You should know what conversion factors you will
need!
b. How many seconds is the average student in class per week?
c. Calculate how many seconds you are in class a day (pick any weekday you have class). Show any
calculations you have to do as dimensional analysis. Answers will vary between you and your classmates.
15. Approximately how many pounds do you weigh? ___________ lbs.
16. A child is entered into the hospital after ingesting 12 aspirin tablets. The Merck Index indicates that renal
(kidney) failure can occur if as little as 3 grams is ingested, and may be fatal if as much as 10 grams is
eaten. If each aspirin tablet contains 300 mg of aspirin, how much aspirin (in grams) has the child
ingested?