Example 6. Calculate: $17.2^{3}+82.3^{3}$ (all numbers are exact)
Solve by consulting a four-figure mathematical table, we get
$$
\begin{array}{l} 
17.2^{3}+82.3^{3}=5.088 \times 10^{3}+5.574 \\
\times 10^{5} \approx 0.0509 \times 10^{5}+5.574 \times 10^{5} \\
\approx 5.625 \times 10^{5} .
\end{array}
$$