You don't always have to change units

When we start learning physics in school, I think we're usually told to convert all quantities into SI base units (metres, kilograms and so forth).  This isn't bad advice as it can certainly prevent some problems.  But it's not always optimal.  And at some point, when we delve more deeply into a particular branch of physics, we will need to become comfortable with somewhat "niche" units.

A simple example of sticking to non-base units is the measurement of density.  Suppose I am given a small cuboid of some material and asked to measure its density.  I get a ruler and measure its dimensions:

3.5 cm x 2.2 cm x 4.7 cm

I put the sample on an electric balance and find its mass to be

120 g

These units -- centimetres and grams -- are what my tools use.  If I convert into metres and kilograms, here's what my calculation looks like:

If instead I'm a bit more sophisticated, I can stay in my original units:

The second method is more efficient: there's simply less writing to do!  And the final number is more elegant too: it turns out grams per cubic centimetre is a natural way to talk about the density of everyday objects.

This tip is very much context specific.  But it's worth asking yourself these questions before you convert units: Do I need to convert?  Do I want to convert?



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