Question

Encontre a fração geratriz das dízimas periódicas simples a seguir:

a)-2,4444...

b)0,1111...

c)17,8888...

d)-6,3535...

e)0,2929...

f)2,102102...​

Answer 1

Explicação passo-a-passo:

a)-2,4444...

x = -2,44...

10x = -24,44...

10x - x = -24,44... - (-2,44...)

9x = -22

x = -22/9

b)0,1111...

x = 0,11...

10x = 1,11...

10x - x = 1,11... - 0,11...

9x = 1

x = 1/9

c)17,8888...

x = 17,88...

10x = 178,88...

10x - x = 178,88... - 17,88...

9x = 161

x = 161/9

d)-6,3535...

x = -6,3535...

100x = -635,3535...

100x - x = -635,3535... - (-6,3535...)

99x = -629

x = -629/99

e)0,2929...

x = 0,2929...

100x = 29,2929...

100x - x = 29,2929... - 0,2929...

99x = 29

x = 29/99

f)2,102102...

x = 2,102102...

1000x = 2102,102102...

1000x - x = 2102,102102... - 2,102102...

999x = 2100

x = 2100/999

x = 700/333