Answer
$0.599\%$
Work Step by Step
The average density of mercury at $35^{\ \circ}C$ based on the measurement results is:
$$\frac{13.56\text{ g}\cdot\text{cm}^{-3}+13.62\text{ g}\cdot\text{cm}^{-3}+13.59\text{ g}\cdot\text{cm}^{-3}}{3}=13.59\text{ g}\cdot\text{cm}^{-3}$$
The true density of mercury at $35^{\ \circ}C$ is $13.509\text{ g}\cdot\text{cm}^{-3}$; thus:
$$\text{percentage error}=\frac{13.59\text{ g}\cdot\text{cm}^{-3}-13.509\text{ g}\cdot\text{cm}^{-3}}{13.509\text{ g}\cdot\text{cm}^{-3}}\cdot 100=0.599\%$$
(Note, percent error is always a positive quantity, so if the equation gives a negative value, the value should be changed to a positive value.)
