Question

Dê a gentriz das dezimas periódica composta.

A)9,22444
B)4,34242
C)5,2999
D)13,888
E)10,311414

Answer 1

a)
$x=9,22444...\\ 100x=922,444...\\ 100x=922+0,444...\\ 100x=922+\frac{4}{9}\\ 100x=\frac{8302}{9}\\ x=\frac{8302}{900}$

b)
$x=4,34242...\\ 10x=43,4242...\\ 10x=43+0,4242...\\ 10x=43+\frac{42}{99}\\ 10x=\frac{4299}{99}\\ x=\frac{4299}{990}$

c)
$x=5,2999...\\ 10x=52,999...\\ 10x=52+\frac{9}{9}\\ 10x=52+1\\ 10x=53\\ x=5,3$

d)
$x=13,888...\\ x=13+0,888...\\ x=13+\frac{8}{9}\\ x=\frac{125}{9}$

e)
$x=10,311414...\\ 100x=1031,1414...\\ 100x=1031 + 0,1414...\\ 100x=1031+\frac{14}{99}\\ 100x=\frac{102083}{99}\\ x=\frac{102083}{9900}$