Dimensional Analysis

Dimensional analysis is the use of units, or dimensions, to set up a problem.

The steps for most 2-step problems without complex units are...

1. Write the unknown...what the problems is converting to or solving for.  The known and unknown are usually in the last sentence.  The unknown is usually in a statement like...What is the value...Solve for...Convert to... How many?  Write UK: and the unknown.

2. Write K: and the known value and units.  There may be more than one known piece of information, but the main value that is being converted or the beginning value is what you are looking for.

3. Write 2 blanks with a times symbol between them an = and a third blank.  Most problems can be solved with 2 blanks.  (If it is evident there needs to be more blanks, you can make as many blanks as you need.)

4. Always write the known value and units in the first blank over a denominator of 1.

5. Carry the units only of the known to the next denominator.

6. Place the unknown units only in the top of the second blank and after the equals, since the unknown is part of the answer.

7. Look carefully at the second blank and try to find a real and true value for the numerator and denominator that makes an accurate conversion factor.

8. Fill in the numbers and do the math.

9. Round to the correct significant figures and box your answer with the correct units.

EXAMPLE:

UK:

K:

known value and units     X                    unknown units only   =     unknown units only

1                                                    known units only

Fill in the conversion factor with numbers that reflect the correct ratio of the unknown units to known units and then do the math.

Multiple Step Problems...

For multi-step problems, there is not a single conversion factor for the units involved... to do these, you follow the steps above, but you will draw more than 2 blanks between the first blank and the =.  Each time you use a conversion factor, the unit in the numerator will appear in the next denominator until you get to the units of the answer.

GO BACK TO DIMENSIONAL ANALYSIS BEGINNING

Complex Unit Problems

A complex unit is one that has a unit in the numerator and denominator.  The unit is almost always stated with the word 'per' between the two units.  To perform these problems...

write the unkown and known...

write the known value and units as a numerator and denominator (split the first unit in the numerator and the second unit, after the 'per' in the denominator... (the denominator usually has a value of 1)...

Draw 2 or more blanks separated by multiplication symbols then...write the unknown units in the last blank after the = sign and also split it as a numerator and denominator.

Now cover the denominator, in the first blank, and fill in units that will convert the numerator to the required numerator in the answer.

Next cover the numerator and fill in the required units to convert it to the numerator in the answer.

Fill in numbers that are correct for each conversion factor.

Perform the multiplication and division required, round to correct significant figures, and include units in your final answer.

GO BACK TO DIMENSIONAL ANALYSIS BEGINNING

PRACTICE PROBLEMS FOR DIMENSIONAL ANALYSIS AND PROBLEM SOLVING...

GO BACK TO DIMENSIONAL ANALYSIS BEGINNING