# Dividing different units of measurement? [duplicate]

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) Commented Aug 13, 2016 at 15:27
• – user7951
Commented Aug 13, 2016 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. Commented Aug 16, 2016 at 23:01

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.