Dimensional Analysis Extra Credit Problems
In order to convert from one unit to another we use a process called dimensional analysis. The great thing about the metric system is that it is really easy to switch from one unit to another. Unfortunately, if you want to make any conversions within the English system, from the metric system to the English system, or with units of time, you need to use dimensional analysis. It is a very useful skill, and once you understand it you will not forget it. This assignment is for extra credit, and it is worth 13 points. Each answer is worth 1.5 points. You will not earn any points for the problem if the problem is not entirely correct. In order to be entirely correct, you must write down the question and the correct conversion factor, show your work, have the correct final answer, and include the correct units in your final answer. You may use a calculator and round your answers to the nearest tenth of a decimal place. You can find the conversion factors in your textbook. Please turn the assignment in on a sheet of loose leaf paper, and use the correct heading. Here is one example problem in case you forgot from our class demonstrations:Example: 15 hours = ? minutes
Conversion factor: You won't even need to look this one up. There are 60 minutes in 1 hour. So your conversion factor is 1 hour = 60 minutes or 60 minutes = 1 hour. It does not matter how you write it. Both of those conversion factors mean the same thing. Please try to get in the habit of writing the units with your conversion factors. It will make it much easier for you in the long run.
Now you write down 15 hours (this number is the one you were given) and multiply it by the conversion factor. There are two ways to write the conversion factor, and now it matters which way you write it. We want our units to cancel, so since we have hours on top (from the 15 hours) you want to write the conversion factor so that hours is on bottom in the conversion factor.
| 15 hours | x | 60 minutes | = | |
| 1 hour |
Now you to multiply 15 by everything on top of the line and then hit equals on your calculator. Then you need to divide that number by the number below the line. This number will be your final answer. Don't forget to include your units. The hours cancelled, so your units are in minutes now. That is good because in the question I was asking for the number of minutes.
| 15 hours | x | 60 minutes | = | 900 minutes |
| 1 hour |
Do the rest of the problems the same way. Be careful how you write the conversion factor in the problem!
1. 108 quarts = ? liters
2. 24 ounces = ? grams
3. 8 inches = ? centimeters
4. 53 pounds = ? kilograms
5. 118 inches = ? centimeters
6. 97 kilograms = ? pounds
7. 208 milliliters = ? cups
8. 65 grams = ? ounces