Question

determine a fraçao geratriz de cada uma das dizimas periódicas abaixo .
_
a)0,8 b)3,151515... c)0,5222..

d)0,007007007... e)2,4777... f)0,1444..

Minha professora pediu cálculo Disso pfv!!​

Answer 1

a)

Não é dizima periódica

$0,8=\frac{8}{10}\\\\\\\boxed{0,8=\frac{4}{5}}$

b) Periodo: 15

$3,151515...~=~3+0,151515...\\\\3,151515...~=~3+\frac{15}{99}\\\\3,151515...~=~\frac{99~.~3~+~1~.~15}{99}\\\\3,151515...~=~\frac{312}{99}\\\\\boxed{3,151515...~=~\frac{104}{33}}$

c) Periodo: 2

$0,5222...~=~0,5+0,0222...\\\\0,5222...~=~\frac{5}{10}+\frac{2}{90}\\\\0,5222...~=~\frac{9~.~5~+~1~.~2}{90}\\\\\boxed{0,5222...~=~\frac{47}{90}}$

d) Periodo: 700

$0,007007007...~=~\frac{700}{99900}\\\\\boxed{0,007007007...~=~\frac{7}{999}}$

e) Periodo: 7

$2,4777...~=~2+0,4+0,0777...\\\\2,4777...~=~2+\frac{4}{10}+\frac{7}{90}\\\\2,4777...~=~\frac{90~.~2~+~9~.~4~+~1~.~7}{90}\\\\\boxed{2,4777...~=~\frac{223}{90}}$

f) Periodo: 4

$0,1444...~=~0,1+0,0444...\\\\0,1444...~=~\frac{1}{10}+\frac{4}{90}\\\\0,1444...~=~\frac{9~.~1~+~1~.~4}{90}\\\\\boxed{0,1444...~=~\frac{13}{90}}$