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Dimensional Analysis or Unit Factor Method, or Unit Canceling are all names for the same concept. Simply put, the unit determine the math not the numbers. In other words,
UNITS, NOT THE NUMBERS ARE KING
Steps for Solving Mathematical Problems in Chemistry.
1. Write down unknown (units and in more complex problems what substance)
2. Write down all known units including conversion factors
A conversion factor is anything that allows you to go from one unit to another unit(s)For example, density it is a conversion factor between mass (g) and volume (cm3).
3. Setting up the answer. (Will not allow math equations)
- a. Look at units in answer to determine the first thing to write
- If you answer has one units, then you start off with one units (if that one unit is in denominator, then you start with an unit in the denominator)
- If answer has more than one unit, then you need to put down more than one known information
- For example if you answer is ft/s, then you start off with a distance term on the top and a time unit on the bottom
- b. Starting with one unit, you then make parentheses ( ) and then a fraction where you put your known conversion factor to get to known unit to unit you are looking for in answer
- Usually you don't have one conversion factor that will get you from your known unit to unit you are looking for. So you will have do have intermediate units.
- If you have more than one unit, you one unit at a time and do another unit, BUT it is all on the same line (you don't break up the calculation.)
- c. Once you have all the desire units, you are done with adding parentheses.
4. Do math (same math rules apply as in sig fig (SF) and scientific notation (SN) section).
- Remember:
- Number must be in scientific notation if greater than 1E3 or less than 1E-3
- One number before answer in N+1 (one more sig fig as in answer), correct SN and units
- Answer in correct SN, SF and units
5. Check answer to see if has correct units (answering question asked) and number makes physical sense!!!
Example: