Question

2) Encontre a fração geratriz de cada dízima: * a) 0,222... b) 0,2323... c) 2,888... d) 1,125125... e) 0,04242... SOCORRO

Answer 1

Explicação passo-a-passo:

a)

x = 0,222...

10x = 2,222...

10x - x = 2,222... - 0,222...

9x = 2

x = 2/9

b)

x = 0,2323...

100x = 23,2323...

100x - x = 23,2323... - 0,2323...

99x = 23

x = 23/99

c)

2,888... = 2 + 0,888...

x = 0,888...

10x = 8,888...

10x - x = 8,888... - 0,888...

9x = 8

x = 8/9

2,888... = 2 + 8/9 = (18 + 8)/9 = 26/9

d)

1,125125... = 1 + 0,125125...

x = 0,125125...

1000x = 125,125125...

1000x - x = 125,125125... - 0,125125...

999x = 125

x = 125/999

1,125125... = 1 + 125/999 = (999 + 125)/999 = 1124/999

e)

x = 0,04242...

10x = 0,4242...

1000x = 42,4242...

1000x - 10x = 42,4242... - 0,4242...

990x = 42

x = 42/990

x = 7/165