Density and Volume: Quick Review

Key Concepts

To find volume from density, use the relation ρ = m / V, so V = m / ρ. Remember that 1 cm^3 = 1 mL. In measurements, the last reported digit is the uncertain digit and should reflect the precision of the data.

Given Data

Mass = $m = 18 \ \mathrm{g}$; Density = $\rho = 10.5 \ \mathrm{g/cm^{-3}}$.

Volume from Density

Volume is found with $V = \frac{m}{\rho}$. The units yield $V = \frac{\mathrm{g}}{\mathrm{g/cm^{3}}} = \mathrm{cm^{3}}$, and since $1 \ \mathrm{cm^{3}} = 1 \ \mathrm{mL}$, the volume is in milliliters.

Significant Figures

Leading zeros are not significant; placeholder zeros (including trailing zeros without decimal) are not significant in this context. Report the result with the least number of significant figures from the inputs.

Worked Example

Compute $V = \frac{18}{10.5} \ \mathrm{cm^{3}} \approx 1.714 \ \mathrm{cm^{3}} = 1.714 \ \mathrm{mL}$. With significant figures, the least precise input has 2 sig figs (the 18). Therefore, $V \approx 1.7 \ \mathrm{mL}$. The volume uncertainty corresponds to the last reported digit (the '7' in 1.7).