Density
Density is mass per unit volume, a property that identifies a material and determines whether it sinks or floats in a fluid.
Formula
\rho = \frac{m}{V}
Definition
Density tells you how much mass is packed into a certain amount of space: divide the mass by the volume, $\rho = \frac{m}{V}$, with lab units of $\text{g/cm}^3$ (equal to g/mL) or SI units of $\text{kg/m}^3$. It is a characteristic property, the same for a pure substance no matter how large the sample, so it can identify an unknown material; water's density is $1.00\ \text{g/cm}^3$, and an object sinks in water if its density is greater. Density is an intensive ratio that depends on temperature and, for gases, pressure, and its uncertainty combines the relative uncertainties of mass and volume. Experimentally it is best found from the slope of a mass-versus-volume plot across several samples, which averages random error and reveals any systematic offset as a nonzero intercept.
Example
A rock of mass $27\ \text{g}$ and volume $10\ \text{cm}^3$ has density $2.7\ \text{g/cm}^3$, denser than water, so it sinks. An unknown block of $54.0\ \text{g}$ measuring $5.0 \times 2.0 \times 2.0\ \text{cm}$ has $V = 20.0\ \text{cm}^3$ and $\rho = 2.7\ \text{g/cm}^3$, matching aluminum, and cutting it in half leaves $27.0\ \text{g}$ in $10.0\ \text{cm}^3$, still $2.7$. Five aluminum pieces with (volume, mass) pairs of $(2.0, 5.4)$, $(4.0, 10.9)$, $(6.0, 16.1)$, $(8.0, 21.7)$, and $(10.0, 27.0)$ in $\text{cm}^3$ and g give a best-fit slope of $2.70\ \text{g/cm}^3$ with an intercept near zero, so there is no evidence of a balance offset, and the slope carries far less uncertainty than any single ratio would.
Key Insight
Things denser than water sink and things less dense float, which is why a steel ship floats: it is mostly hollow, so its overall density is less than water's. Density does not change when you cut a sample in half, because mass and volume both halve, and properties like that are what let you identify substances. Measuring the slope instead of a single ratio is a general lab strategy that turns a one-shot division into a fit that averages error and exposes bias; whenever a quantity is a ratio of two measurables, plot them.