Dimensional Analysis Exercises

Answer the following to the best of your ability. Questions left blank are not counted against you. When you have completed every question that you desire, click the "MARK TEST" button after the last exercise. A new page will appear showing your correct and incorrect responses. If you wish, you may return to the test and attempt to improve your score. If you are stumped, answers to numeric problems can be found by clicking on "Show Solution" to the right of the question.

Do NOT type units into the answer boxes, type only the numeric values. Do NOT use commas or scientific notation when entering large numbers. Answer all non-integer questions to at least 3 significant figures. Correct answers MUST be within ± 1 unit of the third significant figure or they are scored as wrong.



This set of questions uses the conversion factors below (These conversions are EXACT, meaning they are infinitely significant):
1 dozen = 12 things 1 six-pack = 6 drinks 1 case = 24 drinks
  1. 7 Dozen = Donuts
  2. 72 Sodas = Six-packs
  3. 8 Dozen drinks = Cases


  4. This set of questions uses the conversion factors below (These conversions are EXACT, meaning they are infinitely significant):
    1 hour = 60 minutes 1 minute = 60 seconds 1 day = 24 hours
    1 week = 7 days 1 year = 365.25 days 1 century = 100 years

  5. 1 Week = Seconds
  6. 2 Centuries = Minutes
  7. 30 Seconds = Days
  8. 10,000,000 Seconds = Years


  9. This set of questions involves metric prefix interconversion. To review the meanings of each metric prefix, review the Metric Units Lesson. (These conversions are all EXACT, meaning they are infinitely significant):

  10. 1 Gigabyte = Bytes
  11. 1 Micrometer = Hectometers
  12. 1 Kilogram = Milligrams
  13. 1 CentiLiter = DecaLiters


  14. This set of questions uses the conversion factors below. Metric interconversions are assumed to be known (see the Metric Units Lesson). Conversions which are EXACT are stated as such. Otherwise, the significance of the conversion factor is limited by the number of significant figures presented:
    1 mile = 5280 feet (exactly) 1 foot = 12 inches (exactly) 1 inch = 2.54 cm (exactly)
    1 pound = 16 ounces (exactly) 1.00 pound = 454 grams 1 yard = 3 feet (exactly)
    1 gallon = 4 quarts (exactly) 1 pint = 16 fluid ounces (exactly) 1 ton = 2000 pounds (exactly)
    1 quart = 2 pints (exactly) 1.00 Liter = 1.06 quarts 1 milliliter = 1 cm3 (exactly)

  15. 1 Mile = Kilometers
  16. 8 Fl. Ounces = Gallons
  17. 1 Ton = Grams
  18. 35.3 Centiliters = Fl. Ounces
  19. 1 Pound = Milligrams
  20. 1 inch = Millimeters


  21. This set of questions involve multi-dimensional unit conversion using the above conversion factors. To review this type of conversion, see the Dimensional Analysis lesson.

  22. 1 Yd2 = In2
  23. 1 m3 = km3
  24. 1 Ft3 = m3
  25. 327 In3 = L


  26. This set of questions involve conversions in both the numerator and denominator of a combination of units. To review this type of conversion, see the Dimensional Analysis lesson.

  27. 60 miles/hour = ft/s
  28. 925 ft/min2 = m/s2
  29. 5.0 gal/day = mL/min
  30. 1.0 kg/m3 = g/mL
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