Question

Encontre a fração geratriz abaixo e escreva da forma mais irredutível possível: (PRECISO DO CALCULO, ATENÇAO, COM O CALCULO) a) 0,82222... b) 1,4444... c) 0,767676... d) 3,7535353... e) 0,187656565...

Answer 1

Olá!!  :)

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ITEM (A):

$\sf x \ = \ 0,82222...$  

$\sf 10x \ = \ 8,2222...$

$\sf 10x \ = \ 8 \ + \ \frac{2}{9}$

$\sf 10x \ = \ \frac{74}{9}$

Fração geratriz:   $\sf \frac{74}{9}$

Prova real:  

$\sf 10x \ = \ \frac{74}{9} \\\\ 10x \ = \ 8,22222... \\\\ \boxed{x \ = \ 0,822222... \ \ \checkmark}$

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ITEM (B):

 $\sf x \ = \ 1,4444... \\\\ x \ = \ 1 \ + \ \frac{4}{9} \\\\ x \ = \ \frac{13}{9}$

Fração geratriz:  $\frac{13}{9}$

Prova real:     $\sf \frac{13}{9} \ = \ 1,4444... \ \ \checkmark$

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ITEM (C):

$\sf x \ = \ 0,767676... \\\\ 100x \ = \ 76,767676... \\\\ 99x \ = \ 76 \\\\ x \ = \ \frac{76}{99}$

Fração geratriz:   $\sf \frac{76}{99}$

Prova real:   $\frac{76}{99} \ = \ 0,767676... \ \ \checkmark$

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ITEM (D):

$\sf x \ = \ 3,75353535... \\\\ 100x \ = \ 375,353535... \\\\ 100x \ = \ 375 \ + \ \frac{35}{99} \\\\ 100x \ = \ \frac{37.160}{99}$

Fração geratriz:  $\sf \frac{37.160}{99}$

Prova real:

$\sf 100x \ = \ \frac{37.160}{99} \\\\ 100x \ = \ 375,353535... \\\\ \boxed{x \ = \ 3,75353535... \ \ \checkmark}$

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ITEM (E):

$\sf x \ = \ 0,187656565... \\\\ 1.000x \ = \ 187,656565... \\\\ 1.000x \ = \ 187 \ + \ \frac{65}{99} \\\\ 1.000x \ = \ \frac{18.578}{99}$

Fração geratriz:   $\sf \frac{18.578}{99}$

Prova real:

$\sf 1000x \ = \ \frac{18.578}{99} \\\\ 1000x \ = \ 187,656565... \\\\ \boxed{x \ = \ 0,187656565... \ \ \checkmark}$

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Espero ter ajudado, bons estudos!!  :)