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Argon, a noble gas found in the Earth's atmosphere, plays a vital role in various scientific applications due to its inertness. However, to use argon effectively, it's crucial to understand its atomic mass. The atomic mass of argon is approximately 39.95 atomic mass units (u), a value that can be found on the periodic table. This measurement reflects the average mass of all the isotopes of argon, weighted by their respective abundances.

It's essential to recognize that atomic mass is different from atomic number, which is the count of protons in an atom's nucleus. Atomic mass takes into account both protons and neutrons, as their masses are quite similar. Knowing the atomic mass is fundamental when computing the molar mass of substances, thereby enabling chemists to measure the amount of substance in moles, which is a key step in many stoichiometric calculations.

When working in chemistry, it's often necessary to convert the atomic mass from atomic mass units to grams to understand a substance's mass on a macroscopic scale. To perform this conversion, we use a standard conversion factor. This conversion factor is the mass of one atomic mass unit in grams, which is approximately \(1.6605 \times 10^{-24}\) grams.

To convert the atomic mass of argon from atomic mass units to grams, you simply multiply the atomic mass in atomic mass units by the conversion factor: \(39.95\,u \times 1.6605 \times 10^{-24}\,\frac{grams}{u}\). This calculation bridges the gap between the minuscule mass scale of atoms and the more familiar gram scale which is easier to conceptualize and work with in a laboratory setting.

Significant figures are used in science to indicate the precision of a measurement. When performing calculations, it's essential to manage significant figures correctly to ensure that the precision of the final answer reflects the precision of the initial data. In the context of the atomic mass of argon, after converting to grams, the calculated value might have more digits than necessary.

Therefore, when the mass of argon is computed as \(6.64 \times 10^{-23}\) grams, rounding to three significant figures gives us \(6.64 \times 10^{-23}\) grams. The choice of three significant figures correlates with the initial data's precision, indicating that the answer should be reported with the same level of accuracy. This ensures that the data presented is both meaningful and reliably conveys the measurement's accuracy without implying an unwarranted level of precision.