$$3+ \frac{ 4 }{ 34 }$$
$\frac{53}{17}\approx 3.117647059$
$$3+\frac{2}{17}$$
$$\frac{51}{17}+\frac{2}{17}$$
$$\frac{51+2}{17}$$
$$\frac{53}{17}$$
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$\frac{53}{17} = 3\frac{2}{17} = 3.1176470588235294$