Respuesta:
[tex]\frac{16}{5}[/tex]
Explicación paso a paso:
Expresamos los decimales periodicos puros en fracciones:
[tex]10(\frac{x}{y} ) = 1.111...[/tex]
[tex]-\frac{x}{y} =- 0.111...[/tex]
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[tex]9 (\frac{x}{y} ) = 1[/tex]
[tex]\frac{x}{y} = \frac{1}{9}[/tex]
[tex]0.111... = \frac{1}{9}[/tex]
[tex]10(\frac{a}{b} ) = 3.333....[/tex]
[tex]-\frac{a}{b} =- 0.333...[/tex]
__________________
[tex]9(\frac{a}{b} ) = 3[/tex]
[tex]\frac{a}{b} = \frac{3}{9} = \frac{1}{3}[/tex]
[tex]0.333... = \frac{1}{3}[/tex]
Expremos el decimal terminar en fracción:
[tex]\frac{p}{q} = 2.2[/tex]
[tex]10(\frac{p}{q} ) =22[/tex]
[tex]\frac{p}{q} = \frac{22}{10}[/tex]
[tex]\frac{p}{q} = \frac{11}{5}[/tex]
LUEGO:
[tex](\frac{0.111...}{0.333..} X \sqrt[4]{81} )+ 2.2 = \frac{\frac{1}{9} }{\frac{1}{3} } X \sqrt[4]{3^{4} } +\frac{11}{5}[/tex]
[tex]= \frac{1*3}{1*9} * 3^{\frac{4}{4} } +\frac{11}{5} = \frac{3}{9} * 3 + \frac{11}{5}[/tex]
[tex]= \frac{9}{9} + \frac{11}{5} = 1 + \frac{11}{5}[/tex]
[tex]= \frac{5+11}{5}[/tex]
RESPUESTA:
[tex]\frac{16}{5}[/tex]
