Example 2
Silicon has three naturally-occurring isotopes: $92.23 \%$ of $^{28} \mathrm{Si}$, with an atomic weight of 27.9769 amu, $4.68 \%$ of $^{29} \mathrm{Si}$, with an atomic weight of 28.9765 amu, and $3.09 \%$ of $^{30} \mathrm{Si}$ with an atomic weight of 29.9738 amu. On the basis of these data, confirm that the average atomic weight of $\mathrm{Si}$ is 28.0854 amu.