Question

As frações geratriz correspondentes das dízimas periódicas a)- 0,4444........ b) 2,3333........ c) 1,2323232....... são?
10 pontos
a= -4/9 b= 21/9 c= 122/99
a= 4 b= 2/3 c= 1/9
a= -4/9 b= 2/3 c= 123/9
a= -1/4 b= 21/9 c= 1/23​

Answer 1

a)

$x=-0.444\dots\ \to\ 10x=-4.444\dots\ \therefore\\\\ 10x-x=-4.444\dots+0.444\dots\ \therefore\ 9x=-4\ \therefore\ \boxed{x=-\dfrac{4}{9}}$

b)

$x=2.333\dots\ \to\ 10x=23.333\dots\ \therefore\\\\ 10x-x=23.333\dots-2.333\dots\ \therefore\ 9x=21\ \therefore\ \boxed{x=\dfrac{21}{9}}$

c)

$x=1.2323\dots\ \therefore\ 100x=123.2323\dots\ \therefore\\\\ 100x-x=123.2323\dots-1.2323\dots\ \therefore\ 99x=122| \therefore\ \boxed{x=\dfrac{122}{99}}$