Resposta:
a) 37/99
b) 5/9
c) 113/90
Explicação passo-a-passo:
a) x=0,3737...
100.x=37,3737...
100x-x=37,3737... - 0,3737...
99x=37
x=37/99
b) x=0,555...
10.x=5,555...
10x-x=5,555... - 0,555...
9x=5
x=5/9
c) Obs: 1,2555...=1+0,2555...
x=0,2555...
10x=2,555...
Obs: 2,555...=2+0,555...
y=0,555...
10.y=5,555...
10y-y=5,555... - 0,555...
9y=5
y=5/9
10x= 2,555...=2+0,555...=2+y=2+5/9=23/9
10x=23/9 >> 90x=23 >> x=23/90
1,2555...=1+0,2555...=1+x=1+23/90=113/90
