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Dimensional analysis is a problem solving method that uses the math concept that any number or expression multiplied by the number one is unchanged. [1] It is also referred to as the factor-label method or unit factor method. [2]
The key to dimensional analysis is to correctly use units of measurements in solving problems.
Dimensional Analysis has five major steps that need to be followed to convert from one unit to another. The first and second steps are to make a grid then insert the units and labels. The third step is to make an equivalence statement. The fourth step is to use the conversion factors. The last step is to make the calculations.
First Step
The first step in converting units is to make a grid. Add more boxes to the sides of the grid if more are needed. An example would be converting inches to yards. In that case, first inches need to be converted to feet, and then converted feet to yards.
Second Step
The second step is to plug in the given units and then labels. SI units, called the International System, are examples of units that are widely used. [3] Some SI base units are meters for measuring length, liters for measuring volume, and grams for measuring mass.CITATION REQUIRED To avoid confusion when measuring, always specify what units are being measured in. [4] As an example, use the sample problem of converting seven meters to centimeters. First, the numbers are plugged into the grid, then the labels are plugged in the grid and then you use the next step.
Third Step
The third step is to find the equivalence of one unit to another. The conversion, a ratio between two units, for centimeters to meters 100cm.= 1m. or 1m/100cm or 100cm/1m. A metric system and a conversion chart can be helpful when figuring out the conversion factor or equivalence statement.
Fourth Step
The fourth step is to use the conversion factor to figure out the problem. To do this, multiply across the grid and the units cancel each other out. In the example from before you add a 100 to the grid and the meters cancel.
Fifth Step
The fifth step is to calculate the answer. In the last example you multiply the 7 and 100 and then you divide by 1.
Summary
These are the steps to dimensional analysis, a method used to convert units in a measurement system. [5] When converting a certain unit of measurement to another, follow these steps. Here is one last example of dimensional analysis in the form of a picture.
Video
References
- ↑ Math Skills Review Dimensional Analysis. Retrieved January 13, 2009, from Http://www.chem.tamu.edu/class/fyp/mathrev/mr-da.html
- ↑ Fun with Dimensional Analysis. Retrieved January 13, 2009, from http://www.alysion.org/dimensional/fun.html
- ↑ Zumdahl, S.S., Zumdahl, S. L., DeCoste, D. J. (2006). World of Chemistry. Houghton Mifflin Company. p.
- ↑ Felder, Kenny. (1998). One of These Things is Not Like the Other. Retrieved January 13, 2009, from http://www.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/units.html
- ↑ Mathematics VSC Glossary. (1997-2008). Retrieved on January 14, 2009, from http://mdk12.org/instruction/cirriculum/mathematics/glossary.html
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