Question

Encontre a fração geratrix:

A) 0,373737....

B) -0,888....

C) 0,555....

D) -3,222...

E) -1,212121...

F) 0,050505..

G) 0,565656...

H) 1,434343...

I) 2,010101...

Answer 1

A)
a = 0,373737...
100a = 37,3737...

100a - a = 37,373737... - 0,373737...
99a = 37
a = 37/99

B)
b = -0,888...
10b = -8,888...

10b - b = -8,888... + 0,888...
9b = -8
b = -8/9

C)
c = 0,555...
10c = 5,555...

10c - c = 5,555... - 0,555...
9c = 5
c = 5/9

D)
d = -3,222...
10d = -32,222...

10d - d = -32,222... + 3,222...
9d = -29
d = -29/9

E)
e = -1,2121...
100e = -121,2121...

100e - e = -121,2121... + 1,2121...
99e = -120
e = -120/99
Simplificando: -40/33

F)
e = 0,05050...
100e = 5,05050...

100e - e = 5,05050... - 0,05050...
99e = 5
e = 5/99

G)
g = 0,5656...
100g = 56,5656...

100g - g = 56,5656... - 0,5656...
99g = 56
g = 56/99

H)
h = 1,434343...
100h =  143,4343...

100h - h = 143,4343... - 1,4343...
99h = 142
h = 142/99

I)
i = 2,010101...
100i = 201,0101...

100i - i = 201,0101... - 2,0101...
99i = 199
i = 199/99