Question

ENCONTRE AS GERATRIZES DAS SEGUINTES DIZIMAS PERIODICAS: a) 0,555... b)3,535353... c)2,1232323...

Answer 1

$<var>a) 0,555...=\frac{5}{9}</var>$

 

$<var>b)3,535353..=3+0,535353...=3+\frac{53}{99}=\frac{350}{99}</var>$

 

$<var>c)2,1232323...=2+0,1232323=2+\frac{1,232323...}{10}=2+\frac{1+0,232323..}{10}=</var>$

$<var>2+\frac{1+0,232323..}{10}=2+\frac{1+\frac{23}{99}}{10}=\frac{2102}{990}=\frac{1051}{495}</var>$

 

Confira com uma calculadora

Answer 2

 

 

a) 0,555...

          geratriz = 5/9

 

b) 3,535353...

       3 + 0,535353...

        3 + 53/99

        297/99 + 53/99 = 350/99

           geratriz = 350/99

 

c) 2,1232323...

     2 + 0,1232323..

     2 + (123 - 1) / 990

     2 + 122/990

     2 + 61/495

     (990 + 61)/495

         geratriz = 1051/495