Question

Encontre a fração geratriz das dízimas periódicas compostas a seguir a) 7,15555 b) -0,53333 c) 69,0333 d) -1,17474

Answer 1

Explicação passo-a-passo:

a) 7,15555

x = 7,155...

10x = 71,55...

100x = 715,55...

100x - 10x = 715,55... - 71,55...

90x = 644

x = 644/90

x = 322/45

b) -0,53333

x = -0,5333...

10x = -5,333...

100x = -53,333...

100x - 10x = -53,333... -(-5,333...)

90x = -48

x = -48/90

x = - 8/15

c) 69,0333

x = 69,033...

10x = 690,33...

100x = 6903,33...

100x - 10x = 6903,33... - 690,33...

90x = 6213

x = 6213/90

x = 2071/30

d) -1,17474

x = -1,17474...

10x = -11,7474...

1000x = -1174,7474...

1000x - 10x = -1174,7474... - (-11,7474...)

990x = -1163

x = -1163/990