Question

transforme as dizimas periódicas simples em fração geratriz

a) 2,555555...

b) 5,777777

c) 1,787878

d) 6,020202
​

Answer 1

Explicação passo-a-passo:

2,555...=x(10)

25,55...=10x

10x-x=25,55...-2,55...

9x=23

x=>23/9

5,777...=x(10)

57,777...=10x

10x-x=57,777...-5,777...

9x=52

x=>52/9

1,7878...=x(10)

17,8787...=10x(10)

178,78...=100x

100x-x=178,78...-1,7878...

99x=177

x=177/99(÷3)

x=>59/33

6,0202...=x(10)

60,2020...=10x(10)

602,0202...=100x

100x-x=602,0202...-6,0202...

99x=596

x=>596/99