Question

resolva em forma de equação, as 3 dízimas periódicas compostas;
a) 1, 1111...
b) 0, 01111...
c) 2, 12222222...
por favor

Answer 1

Olá, Pietra.

$a)~1,111...=1+0,111...=1+\frac19=\frac{9+1}9=\frac{10}9\\\\ b)~0, 0111...=\frac{0,111...}{10}=\frac1{10}\times0,111..=\frac1{10}\times\frac19=\frac1{90}\\\\ c)~2, 1222...=2,1+0,0222...=\frac{21}{10}+\frac{0,222...}{10}=\frac{21}{10}+\frac29\times\frac1{10}=\\\\=\frac{189+2}{90}=\frac{191}{90}$