$$3+ \frac{ 3 }{ 33 }$$
$\frac{34}{11}\approx 3.090909091$
$$3+\frac{1}{11}$$
$$\frac{33}{11}+\frac{1}{11}$$
$$\frac{33+1}{11}$$
$$\frac{34}{11}$$
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$\frac{2 \cdot 17}{11} = 3\frac{1}{11} = 3.090909090909091$