$$ \begin{aligned} &\text { Calculate the density of magnesium, in } \mathrm{g} / \mathrm{cm}^{3}, \text { if its mass is }\\\ &14.3 \mathrm{~g} \text { and its volume is } 8.46 \mathrm{~cm}^{3} . \end{aligned} $$

Chemistry education forms the basis for understanding the physical properties of matter, one of which is density. Density is a vital concept that explains how much matter is packed into a given volume. For students grappling with chemistry homework, a clear grasp of density can illuminate why certain materials float while others sink, and why some substances feel heavier than others, even if their volume appears the same.

Grasping the essence of density is not just about memorizing formulas; it's about developing an intuitive sense of how atoms and molecules occupy space in different states of matter. This comprehension is critical when progressing to more complex topics in science and engineering, where density plays a pivotal role in material selection, buoyancy calculations, and even in understanding astronomical phenomena such as planet formation.

The key to solving any density problem lies in the density formula: \( \rho = \frac{m}{V} \), where \( \rho \) is the density, \( m \) is the mass, and \( V \) is the volume. When using this formula, it's important to pay attention to the units of mass and volume to ensure they are compatible—mass typically in grams (g) and volume in cubic centimeters (\(cm^3\)) or milliliters (mL), which are equivalent.

For example, to calculate the density of magnesium, you would divide the mass of the magnesium (given in grams) by its volume (given in cubic centimeters). It's a straightforward operation, but its simplicity belies its importance. Density calculations are ubiquitous in laboratory settings to determine the purity of a substance, to identify unknown materials, and to calculate how much of a substance is needed for a reaction.

The concept of significant figures is central to all scientific measurements as it communicates the precision of the recorded data. In chemistry, it's imperative to report measurements and calculations with the correct number of significant figures to maintain the integrity of the results.

In the case of the magnesium density calculation, the mass is provided to three significant figures (14.3 g), which indicates the precision of the measurement. Therefore, the calculated density should also reflect three significant figures, ensuring that the result communicated, \( \rho = 1.69 \frac{g}{cm^3} \) is both precise and accurate according to the initial data. Appropriately rounding and reporting significant figures is not just about following rules—it's about ensuring the communication of data is as precise and useful as possible, which is fundamental in scientific discourse and experimentation.