Question

URGENTE!!! Encontre a fração geratriz de cada dízima periódica e dos decimais exatos.


a) 1,8181...

b)1,354354...

c)0,12525...


Respostas: a) 20/11 b) 451/333 c) 62/495

Answer 1

Olá, tudo bem?

Vamos lá!

$a)x=1,\overline{81}\\ 100x=181,\overline{81}\\\\100x-x=181,81+1,81\\99x=180\\x= \frac{180^{\div9}}{99^{\div9}}\\\\\\\boxed{x= \frac{20}{11}}\\\\\\ b)x=1,\overline{354}\\ 1000x=1354,\overline{354}\\\\1000x-x=1354,354-1,354,354\\ 999x=1353\\ x= \frac{1353^{\div3}}{999^{\div3}}\\\\\boxed{x= \frac{451}{333} }\\\\\\ c)x=0,1\overline{25}\\ 10x=1,\overline{25}\\ 1000x=125,\overline{25}\\\\ 1000x-10x=125,25-1,25\\ 990x=124\\ x= \frac{124^{\div3^}}{990^{\div3}} \\\\ \boxed{x= \frac{62}{495} }$