Problem: The density of a pure substance is its mass per unit volume. The density of ethylene glycol has been measured to be $1097 . \frac{\mathrm{g}}{\mathrm{L}}$. Calculate the mass of $405 . \mathrm{mL}$ of ethylene glycol. Be sure your answer has a unit symbol and the correct number of significant digits.

Step 1 ：The problem is asking for the mass of a certain volume of ethylene glycol. We know the density of ethylene glycol, which is the mass per unit volume. Therefore, we can calculate the mass by multiplying the density by the volume.

Step 2 ：However, we need to make sure that the units of volume are the same in both the density and the volume given. The density is given in grams per liter (g/L) and the volume is given in milliliters (mL). We know that 1 L = 1000 mL, so we can convert the volume to liters before performing the calculation.

Step 3 ：Given density = 1097 g/L and volume = 405 mL, we convert the volume to liters: volume_L = 0.405 L.

Step 4 ：We calculate the mass by multiplying the density by the volume: mass = density * volume_L = 1097 g/L * 0.405 L = 444.285 g.

Step 5 ：The problem asks for the answer to have the correct number of significant digits. The given values have three significant digits, so the final answer should also have three significant digits. Therefore, we round the mass to three significant digits: mass_rounded = 444.29 g.

Step 6 ：Final Answer: The mass of 405 mL of ethylene glycol is approximately \(\boxed{444.29 \, \text{g}}\).