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[tex]\boxed{\begin{array}{l}\sf Determine~a~frac_{\!\!,}\tilde ao~geratriz~das~d\acute izimas~peri\acute odicas:\\\tt a)~\sf 0,8333...\\\tt b)~\sf3,666...\\\tt c)~\sf2,41666...\end{array}}[/tex]
[tex]\tt a)~\sf k=0,8333...\cdot10\\\sf 10k=8,333...\cdot10\\\sf100k=83,333....\\-\underline{\begin{cases}\sf100k=83,333...\\\sf 10k=8,333...\end{cases}}\\\sf90k=75\\\sf k=\dfrac{75\div15}{90\div15}\\\huge\boxed{\boxed{\boxed{\boxed{\sf k=\dfrac{5}{6}}}}}\checkmark[/tex]
[tex]\tt b)~\sf\ell =3,666...\cdot10\\\sf 10\ell=36,666...\\-\underline{\begin{cases}\sf10\ell=36,666...\\\sf\ell=3,666...\end{cases}}\\\sf 9\ell=33\\\sf \ell=\dfrac{33\div3}{9\div3}\\\huge\boxed{\boxed{\boxed{\boxed{\sf\ell=\dfrac{11}{3}}}}}\checkmark[/tex]
[tex]\tt c)~\sf\Re=2,41666...\cdot100\\\sf 100\Re=241,666...\cdot10\\\sf1000\Re=2416,66...\\-\underline{\begin{cases}\sf 1000\Re=2416,666...\\\sf100\Re=241,666...\end{cases}}\\\sf 900\Re=2175\\\sf\Re=\dfrac{2175\div75}{900\div75}\\\huge\boxed{\boxed{\boxed{\boxed{\sf\Re=\dfrac{29}{12}}}}}\checkmark[/tex]
