Concept preview

What you will be able to do

1. 01Explain what a derived quantity and derived unit are
2. 02Calculate density, mass or volume using $d = m/V$
3. 03Use density as a conversion factor and predict floating or sinking

A derived quantity is a number made by combining two or more other values, and a derived unit is a unit made by combining two or more other units. For example, the heat absorbed when water is warmed is $\Delta H = c\,m\,\Delta T$, and rearranging for the specific heat capacity gives $c = \dfrac{\Delta H}{m\,\Delta T}$, whose derived units work out to $\mathrm{J\,g^{-1}\,{}^{\circ}C^{-1}}$. You find a derived unit the same way you find the quantity: by substituting the units of each symbol into the equation and simplifying.