Question

Escreva a fração geratriz. A)27,585858... B)3,16434343... C)0,222... 2)ESCREVA NA FORMA DE FRAÇÃO. A)3,444... B)5,454545... C)0,383838... D)4,265353...

Answer 1

1.

a) Periodo = 58

$27,585858...~=~27+0,585858...\\\\\\27,585858...~=~27+\frac{58}{99}\\\\\\27,585858...~=~\frac{99~.~27~+~1~.~58}{99}\\\\\\27,585858...~=~\frac{2673+58}{99}\\\\\\\boxed{27,585858...~=~\frac{2731}{99}}$

b) Periodo = 43

$3,16434343...~=~3,16+0,00434343...\\\\\\3,16434343...~=~\frac{316}{100}+\frac{43}{9900}\\\\\\3,16434343...~=~\frac{99~.~316~+~1~.~43}{9900}\\\\\\3,16434343...~=~\frac{31284+43}{9900}\\\\\\\boxed{3,16434343...~=~\frac{31327}{9900}}$

c) Periodo = 2

$\boxed{0,222...~=~\frac{2}{9}}$

2.

a) Periodo = 4

$3,444...~=~3+0,444...\\\\\\3,444...~=~3+\frac{4}{9}\\\\\\3,444...~=~\frac{9~.~3~+~1~.~4}{9}\\\\\\\boxed{3,444...~=~\frac{31}{9}}$

b) Periodo = 45

$5,454545...~=~ 5+0,454545...\\\\\\5,454545...~=~5+\frac{45}{99}\\\\\\5,454545...~=~\frac{99~.~5~+~1~.~45}{99}\\\\\\5,454545...~=~\frac{540}{99}~~ \rightarrow~Simplificando~por~9\\\\\\\boxed{5,454545...~=~\frac{60}{11}}$

c) Periodo = 38

$\boxed{0,383838...~=~\frac{38}{99}}$

d) Periodo = 53

$4,265353...~=~4,26+0,005353...\\\\\\4,265353...~=~\frac{426}{100}+\frac{53}{9900}\\\\\\4,265353...~=~\frac{99~.~426~+~1~.~53}{9900}\\\\\\\boxed{4,265353...~=~\frac{42227}{9900}}$