Question

(UFPI) Marque a alternativa que contém o valor da expressão numérica
$1.88888... \ + \frac{1}{9}$
a.
$\frac{33}{50}$
b.
$\frac{10}{9}$
c.
$\frac{10}{19}$
d. 2
e.
$\frac{7}{55}$
​

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm Vamos\,encontrar\,a\,geratriz}\\\underline{\rm da \,d\acute izima\,peri\acute odica}\\\sf  x=1,888\dotsc\cdot10\\\sf 10x=18,888\dotsc\\\sf 10x=17+1,888\dotsc\\\sf 10x=17+x\\\sf 10x-x=17\\\sf 9x=17\\\sf x=\dfrac{17}{9}\\\underline{\rm substituindo\,na\,express\tilde ao\,temos:}\\\sf 1,888\dotsc+\dfrac{1}{9}=\dfrac{17}{9}+\dfrac{1}{9}=\dfrac{17+1}{9}=\dfrac{18}{9}=2\end{array}}$