Question

Determine a fração geratriz de cada uma das dízimas periódicas abaixo
a) 0 44444
b) 0.12525
9222
C) 0.545454
d) 0.04777
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Answer 1

a) 0,44444=x.(10)

04,44444=10x

10x-x=4,44444-0,44444

9x-4

(Isola o x)

x=4/9

c)0,545454=x.(10)

05,454545=10x.(10)

054,545454=100x

100x-x=054,545454-0,545454

99x-54

x=54/99

x=18/33

x=6/11

d)0,04777=x.(10)

00,47777=10x.(10)

004,7777=100x.(10)

0047,7777=1000x

1000x-100x=0047,777-004,777

x=