# Unit Conversions Practice Problems

*Jump down to:*Density | Scale

## Some simple unit conversion problems

If you do not have a list of common conversion factors in your book, you may wish to download and print this sheet of common conversion factors for the geosciences (Acrobat (PDF) PRIVATE FILE 40kB Sep3 09). open the link below to use while you make your calculations.

If you need a reminder of the steps, you can download and print this worksheet (Acrobat (PDF) PRIVATE FILE 44kB Apr11 08) walking you through the steps for unit conversion.

Finally, you can download a sheet that has all the problems (Acrobat (PDF) 48kB Jul25 09) on it so you can print it out and work them on your own.

If you need a reminder of the steps, you can download and print this worksheet (Acrobat (PDF) PRIVATE FILE 44kB Apr11 08) walking you through the steps for unit conversion.

Finally, you can download a sheet that has all the problems (Acrobat (PDF) 48kB Jul25 09) on it so you can print it out and work them on your own.

## Rate Problems

**Problem 1:**Imagine that you are driving your car in Canada. As you're driving along, you notice that the speed limit signs have numbers like 120 (on the highway) and 50 (in the city). As you start to speed up, you realize that the signs are in km/hour. Unfortunately, your speedometer only reads in mi/hour. Figure out how fast you're allowed to go if the sign says:

- 120 km/hr
- 75 km/hr
- 50 km/hr

## Density Conversions *(multiple step problems)*

**Problem 2:**Geologists' observations suggest that the two most common rocks exposed at the surface of the Earth are granite (continental crust) and basalt (oceanic crust). From travel times of earthquake waves, we also know that the average density of the Earth is about 5.5 g/cm

^{3}. See if you can do some unit conversions using information given in the questions below to determine whether the whole Earth could be made of these two rock types only.

- As an astute observer walking around on continental crust (granite), you might decide to test the hypothesis that the Earth is made entirely of granite. You weigh a 1.00 cubic ft piece of granite on your home scale and find that it weighs 171 lbs. Thus you determine that the granite has a density of 171 lb/ft
^{3}. Convert your granite's density to g/cm^{3}. Given the information above, could the earth be made completely of granite? - Given that basalt seems to well up when ocean crust pulls apart at Mid-Ocean ridges, you might decide that maybe the entire Earth is made of basalt. On your bathroom scale, a 64 in
^{3}(4in x 4in x 4in) block of basalt weighs 116 ounces. Use this information to calculate whether the average density of the Earth (5.5 g/cm^{3}) can be explained by an Earth made completely of basalt.

## Scaling problems

**Problem 3:**You are working with a map that has a fractional scale of 1:24,000 (meaning that 1 unit on the map is equal to 24,000 units on the ground - 1mm = 24,000 mm or 1 in = 24,000 in). See if you can determine solutions to the following problems that geologists face when working with maps.

- You are hiking to a field area and measure the length of the trail as 18.5 inches. Calculate how many miles you have to hike to get to the interesting rocks/geology?
- Once you get to your field area, you are going to create a geologic map of that area. You have a mechanical pencil that has a lead that is 0.3 mm thick. The smallest feature you can map will be something that is 0.3 mm wide on the map. How wide (in m) can that feature be?
- Now you have an idea of the size of features that can be drawn on your map. Convert your answer in problem 3.2 to feet.

## Next Steps

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## Still need more practice?

There are numerous websites that have practice problems for unit conversions. Several of them are listed below. Please use these links for more practice with unit conversions!

- Dr. Crystal Yau in the chemistry department at Community College of Baltimore County, has a worksheet that you can download called Practice problems on Unit Conversions (Acrobat (PDF) PRIVATE FILE 110kB Oct9 07). The answers are included.
- The Science Spot's Metric Mania Page has two worksheets that have unit conversion practice problems (answers are provided, but not worked through):
- English or Metric? (Acrobat (PDF) PRIVATE FILE 5kB Oct9 07) | Conversion within Metric System (Acrobat (PDF) PRIVATE FILE 8kB Oct9 07)

- Oak Road Systems has several practice problems with answers (but not worked through).
- Scott Van Bramer at Weidner University has a number of links to unit conversion practice problems from length to volume and so on. You can check your answers within the practice webpages.
- Jerry Artz at Hamline College has sample Unit Conversion problems, problem set 1 with some complex unit conversions and Problem set 2 with word problems. All of these links include answers.
- The School of Technology at Purdue University has three sets of Unit Conversion Practice problems. Answers are provided but not worked through.
- Math Goodies has a worksheet with some word problems having to do with dimensional analysis. Link to answer key in the box below the image of the worksheet.
- Alan's Chemistry page has some quizzes (take Quiz 4 or 5) that deal with dimensional analysis (and significant figures).