$$5+ \frac{ 4 }{ 10 } + \frac{ 2 }{ 100 } =$$
$\frac{271}{50}=5.42$
$$5+\frac{2}{5}+\frac{2}{100}$$
$$\frac{25}{5}+\frac{2}{5}+\frac{2}{100}$$
$$\frac{25+2}{5}+\frac{2}{100}$$
$$\frac{27}{5}+\frac{2}{100}$$
$$\frac{27}{5}+\frac{1}{50}$$
$$\frac{270}{50}+\frac{1}{50}$$
$$\frac{270+1}{50}$$
$$\frac{271}{50}$$
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$\frac{271}{2 \cdot 5 ^ {2}} = 5\frac{21}{50} = 5.42$
