$$9+\frac{15}{111}\Rightarrow$$
$\frac{338}{37}\approx 9.135135135$
$$9+\frac{5}{37}$$
$$\frac{333}{37}+\frac{5}{37}$$
$$\frac{333+5}{37}$$
$$\frac{338}{37}$$
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$\frac{2 \cdot 13 ^ {2}}{37} = 9\frac{5}{37} = 9.135135135135135$
