Question

Determine a fração geratriz de cada dezima periodica

a) 10,8
b) 9,7272
c) 25,103103
d) 6,87
e) 50,33424242​

Answer 1

Explicação passo-a-passo:

A) 10,8 (período)

x= 10,88888...

10x= 108,8888...

10x= 108,8888...

-x= 10,88888...

9x= 98

x= 98/9

B) 9,727272...

x= 9,727272...

100x= 972,727272...

100x= 972,727272...

- x= 9,727272...

99x= 963

x= 963/99

x= 321/33

C) 25,103103103...

x= 25,103103103...

1000x= 25103,103103...

1000x= 25103,103103...

-x= 25,103103103...

999x= 25078

x= 25078/999

D) 6,87 (período)

x=6,878787

100x= 687,878787...

100x= 687,878787...

-x=6,878787...

99x= 681

x= 681/99

x= 227/33

E) 50,33424242...

x= 50,33424242...

100x= 5033,424242...

10000x= 503342,424242...

10000x= 503342,424242...

- 100x= 5033,424242...

9900x= 498309

x= 498309/9990

x= 166103/3300