$$9\frac{1}{9}\times10\frac{1}{3}\times5\frac{1}{2}$$
$\frac{13981}{27}\approx 517.814814815$
$$\frac{81+1}{9}\times \frac{10\times 3+1}{3}\times \frac{5\times 2+1}{2}$$
$$\frac{82}{9}\times \frac{10\times 3+1}{3}\times \frac{5\times 2+1}{2}$$
$$\frac{82}{9}\times \frac{30+1}{3}\times \frac{5\times 2+1}{2}$$
$$\frac{82}{9}\times \frac{31}{3}\times \frac{5\times 2+1}{2}$$
$$\frac{82\times 31}{9\times 3}\times \frac{5\times 2+1}{2}$$
$$\frac{2542}{27}\times \frac{5\times 2+1}{2}$$
$$\frac{2542}{27}\times \frac{10+1}{2}$$
$$\frac{2542}{27}\times \frac{11}{2}$$
$$\frac{2542\times 11}{27\times 2}$$
$$\frac{27962}{54}$$
$$\frac{13981}{27}$$
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$\frac{11 \cdot 31 \cdot 41}{3 ^ {3}} = 517\frac{22}{27} = 517.8148148148148$
