Dividing different units of measurement?

Question

1) $$\frac{35 \; \text{cm}^2}{0.62 \; \text{cm}} = 56.4516$$

For the units in the answer, do you put $56.4516$ cm$^2$ or just $56.4516$ cm?

1) $$\frac{0.075 \; \text{g}}{0.0003 \; \text{cm}^3} = 250$$ Same here, do you put $250$ g, $250$ cm$^3,$ or $250$ g/cm$^3$?

You can do 'math' with units in the same way you do with numbers... if the units are the same then the indices can add/subtract when multipled/divided. If not, then you just string them together (or convert the units so they match) — NotEvans., Aug 13 '16 at 15:27
Related: May I treat units (e.g. joules, grams, etc.) in equations as variables? — , Aug 13 '16 at 15:59
as well as treating units as variables you need to consider the number of decimal places you quote in your answers relative to the number of significant digits in the numbers. — porphyrin, Aug 16 '16 at 23:01

score 0 · Answer 1 · answered Aug 13 '16 at 15:32

What does $g/cm^3$ mean? It means you have divided a mass in grams by a volume in $cm^3$ (the slash character"/" is really a division). So yes, your second value is 250 $g/cm^3$.

In the first case, you can simplify $cm^2/cm$, just like in any equation, to $cm$. So your value is 56.4516 cm.

Dividing different units of measurement?

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