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Group Activity:
Dimensional Analysis Part 1

Linear Measure
2.54 cm = 1 in
12 in = 1 ft
5280 ft = 1 mi
0.3048 m = 1 ft
1 km = 0.621 mi
1 furlong = 660 ft
3 ft = 1 yd
0.0394 in = 1 mm
Weight/Mass
1 stone = 14 lbs
1 lb = 0.4536 kg
1 oz = 16 drams
1 oz = 28.35 g
16 oz = 1 lb
2,000 lbs = 1 ton
1 oz = 28,350 mg
1 carat = 0.2 g
Volumetric Measure
1 cup = 16 tablespoons
2 cups = 1 pint
2 pints = 1 quart
1 gal = 4 quarts
1 gal = 3.78 L
1 mL = 1 cm3
1 m3 = 1000 L
1 cup = 236.6 mL
Time
1,000 ms = 1 s
60 s = 1 min
60 min = 1 hr
24 hr = 1 day
365 day = 1 yr
14 days = 1 fortnight
10 yr = 1 decade
100 yr = 1 century

Do the following conversions using the unit factor process. Show your work for each step and cancel out units as you work. The point of this lesson is not just getting the right result, which you could find on the Internet anyway. The point is to learn how to set up and carry out unit conversion. This is a useful skill and will be used throughout your chemistry course.

Do all work on a separate piece of paper and number each problem clearly.


Basic Conversions
  1. Convert 4,200 ft to furlongs
  2. Convert 116 cm to ft
  3. Convert 64 ft to m
  4. Convert 2,512 yd to mi
  5. Convert 13.6 stone to kg
  6. Convert 175 drams to g
  7. Convert 0.875 kg to oz
  8. Convert 54 km to ft
  9. Convert 42 tbsp to quarts
  10. Convert 0.5 L to pints
  11. Convert 788,400,000 seconds to years
  12. Convert 1,250 cm3 to quarts

Custom Conversion Factors

It often happens that in doing different conversions, we use the same long sequence of conversion factors. There is a way to simplify and speed up the process of completing a conversion. To do so, we simply convert one unit into many smaller units to create a new conversion factor. Create the following conversion factors by combining conversions from the table.

  1. Convert 1 hr to s and fill in:
    1 hr = _____ s
  2. Convert 1 gal to cups and fill in:
    1 gal = _____ cups
  3. Convert 1 gal to mL and fill in:
    1 gal = _____ mL
  4. Convert 1 mi to m and fill in:
    1 mi = _____ m
  5. Convert 1 ft to cm and fill in:
    1 ft = _____ cm
  6. Convert 1 lb to g and fill in:
    1 lb = _____ g

Using Custom Conversions

Now, use those custom conversions to do things in just one step!

  1. Convert 9600 s to hr
  2. Convert 42 cups to gal
  3. Convert 0.125 gal to mL
  4. Convert 3100 m to mi
  5. Convert 182 cm to ft
  6. Convert 3,200 g to lb


Dimensional Analysis Part 2
Dimensional Analysis Part 3
Metrics Units are treated in a separate activity.
Additional Dimensional Analysis Problems
First Dimensional Analysis Homework
Activity: Dimensional Analysis with Word Problems
Second Dimensional Analysis Homework
After that homework, practice your skills with the problems on this page from Science by Jones: http://www.sciencebyjones.com/dimensional_analysis_problems.htm
Square and Cubic Units Homework
Density, Part 1
Density: Additional Problems
Last updated: Sep 29, 2026 Home
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