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Vamos là.

a)

x = 0.414141...

100x = 41,414141...

99x = 41

x = 41/99

b)

x = 0,555...

10x = 5

9x = 5

x = 5/9

4,555... = 4 + 5/9 = 41/9

c)

x = 0,212121...

100x = 21,212121...

99x = 21

x = 21/99 = 7/33

3 + 7/33 = 106/33

d)

x = 0,898989...

100x = 89,898989...

99x = 89

x = 89/99

17,898989... = 17 + 89/99 = 1772/99