You can use units to check your work. You often will need to use different versions of a formula, or use a string of formulas, to solve a physics problem. To check that you have set up a problem correctly, write out the equation or set of equations you plan to use. Before performing calculations, check that the answer will be in the expected units, as shown in step 3 of Example Problem 1. For example, if you are finding a speed and you see that your answer will be measured in s/m or m/s², you know you have made an error in setting up the problem. This method of treating the units as algebraic quantities, which can be cancelled, is called dimensional analysis.

Dimensional analysis also is used in choosing conversion factors. A conversion factor is a multiplier equal to 1. For example, because 1 kg = 1000 g, you can construct the following conversion factors:

$1 = \frac{1\ \text{kg}}{1000\ \text{g}} \quad \text{or} \quad 1 = \frac{1000\ \text{g}}{1\ \text{kg}}$

Choose a conversion factor that will make the units cancel, leaving the answer in the correct units. For example, to convert 1.34 kg of iron ore to grams, do as shown below:

$1.34 \cancel{kg} \times \left( \frac{1000g}{1 \cancel{kg}} \right) = 1340\ \text{g}$

You also might need to do a series of conversions. To convert 43 km/h to m/s, do the following:

$\left( \frac{43\ \cancel{km}}{1\ \bcancel{h}} \right) \times \left( \frac{1000\ \text{m}}{\cancel{1\ \text{km}}} \right) \times \left( \frac{1\ \bcancel{h}}{60\ \xcancel{min}} \right) \times \left( \frac{1\ \xcancel{min}}{60\ \text{s}} \right) = 12\ \text{m/s}$