Dimensional Analysis – Multiple Steps

Sometimes it takes two or more steps to convert units.

Example Problem: convert 25.3 cm to km.

If you don’t know a direct conversion factor to get from cm to km, convert to meters first (1 m = 100 cm).

Solution Step 1:

\cfrac{25.3 \, \cancel{cm}}{1} \times \left(\cfrac{1\,m}{100 \, \cancel{cm}}\right)

Now cm has canceled out. We could multiply it out to see how many meters it is, but we don’t need to. Instead, multiply by a second conversion factor to get from m to km (1 km = 1000 m).

Solution Step 2:

\cfrac{25.3 \, \cancel{cm}}{1} \times \left(\cfrac{1\,\cancel{m}}{100 \, \cancel{cm}}\right) \times \left(\cfrac{1\,km}{1000\,\cancel{m}}\right) = \SI{0.000253}{km}

Now meters cancels and leaves an answer in kilometers.

<– Previous: Dimensional Analysis   /   Next: Squared Units –>