Question

A fração geratriz da dízima periódica 0,01111... é:
A)1/5
B)1/9
c)1/10
D)1/ 90
E) 8/9

Answer 1

Resposta:

$0.0\bar1=\frac{1}{90}$

Explicação passo a passo:

$0.0\bar1=0.01+0.00\bar{1}=0.01+\frac{0.0\bar{1}}{10}$

vamos chamar $0.0\bar1$ de $x$, então

$x=0.01+\frac{x}{10}\\\\x-\frac{x}{10}=0.01\\\\\frac{10}{10}\times x-\frac{x}{10}=0.01\\\\\frac{10\times x}{10}-\frac{x}{10}=0.01\\\\\frac{10x-x}{10}=0.01\\\\\frac{9x}{10}=0.01\\\\9x=0.01\times10\\\\9x=0.1\\\\x=\frac{0.1}{9}\\\\x=\frac{0.1}{9}\times\frac{10}{10}\\\\x=\frac{1}{90}$

então, como chamamo $0.0\bar1=x$ e $x=\frac{1}{90}$, então $0.0\bar1=\frac{1}{90}$

Qualquer coisa grita nois