Question

1. Calcule a fração geratriz de cada uma das dízimas periódicas simples abaixo

(SIMPLIFIQUE A FRAÇÃO QUANDO NECESSÁRIO):

a) 0,55555…

b) 2,444444…

c) 25,222222…

d) 3,1111….​

Answer 1

$\Large\boxed{\begin{array}{l}\rm a)\\\sf x=0,555\dotsc\cdot10\\\sf 10x=5,555\dotsc\\-\underline{\begin{cases}\sf 10x=5,555\dotsc\\\sf ~~~x=0,555\dotsc\end{cases}}\\\sf 9x=5\\\sf x=\dfrac{5}{9}\end{array}}$

$\Large\boxed{\begin{array}{l}\rm b)\\\sf x=2,444\dotsc\cdot10\\\sf 10x=24,444\dotsc\\-\underline{\begin{cases}\sf 10x=24,444\dotsc\\\sf ~~~x=2,444\dotsc\end{cases}}\\\sf 9x=22\\\sf x=\dfrac{22}{9}\end{array}}$

$\Large\boxed{\begin{array}{l}\rm c)\\\sf x=25,222\dotsc\cdot10\\\sf 10x=252,222\dotsc\\-\underline{\begin{cases}\sf 10x=252,222\dotsc\\\sf ~~~x=25,222\dotsc\end{cases}}\\\sf 9x=227\\\sf x=\dfrac{227}{9}\end{array}}$

$\Large\boxed{\begin{array}{l}\rm d)\\\sf x=3,111\dotsc\cdot10\\\sf 10x=31,111\dotsc\\-\underline{\begin{cases}\sf 10x=31,111\dotsc\\\sf~~~ x=3,111\dotsc\end{cases}}\\\sf 9x=28\\\sf x=\dfrac{28}{9}\end{array}}$