Question

3- Escreva a fração geratriz das dizimas periódicas.
a)0,333...
b)1,454545...
c)0,1222...
d)2,8333...​

Answer 1

Explicação passo-a-passo:

0,333...=x(10)

3,333...=10x(10)

33,333...=100x

100x-10x=33,333...-3,333...

90x=30

x=30÷30/90÷30

x=1/3

1,454545...=x(10)

14,545454...=10x(10)

145,454545...=100x

100x-x=145,454545...-1,454545...

99x=144

x=144÷9/99÷9

x=16/11

0,1222...=x(10)

1,222...=10x(10)

12,222...=100x

100x-10x=12,222...-1,222...

90x=11

x=11/90

2,8333...=x(10)

28,333...=10x(10)

283,333...=100x

100x-10x=283,333...-28,333...

90x=255

x=255÷15/90÷15

x=17/6

Answer 2

a) 0,333...

Resposta: $\frac{3}{9}$

b) 1,454545...

$1+\frac{45}{99} =\frac{99+45}{99} = \frac{144}{99}$

C) 0,1222... (composta)

x = 0,1222...(10) =>> multiplicado por 10

10x = 1,222...(10) =>> multiplicado por 10

100x = 12,222...

Subtrair:

100x = 12,222...

- 10x =   1,222...

90x =   11

resposta:  $\frac{11}{90}$

D) 2,8333... (composta)

x = 2,8333... (10)

10x = 28,333...(10)

100x = 283,333...

Subtrair:

100x = 283,333...

- 10x =    28,333...

 90x =   255

resposta: $\frac{255}{90}$

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Respostas já simplificadas:

A) $\frac{1}{3}$

B) $\frac{16}{11}$

C) $\frac{11}{90}$

D) $\frac{17}{6}$