Answer
We use $\rho=m / V$ and
$$\Delta \rho=\Delta(m / V)=m \Delta(1 / V) \simeq-m \Delta V / V^{2}=-\rho(\Delta V / V)=-3 \rho(\Delta L / L)$$
The percent change in density is
$$\frac{\Delta \rho}{\rho}=-3 \frac{\Delta L}{L}=-3(0.23 \%)=-0.69 \%$$
Work Step by Step
We use $\rho=m / V$ and
$$\Delta \rho=\Delta(m / V)=m \Delta(1 / V) \simeq-m \Delta V / V^{2}=-\rho(\Delta V / V)=-3 \rho(\Delta L / L)$$
The percent change in density is
$$\frac{\Delta \rho}{\rho}=-3 \frac{\Delta L}{L}=-3(0.23 \%)=-0.69 \%$$
