Question

Transforme as seguintes Dizimas periódicas em frações:

1)0,55555....
2)0,33333....
3)0,45454....
4)0,44444....
5)0,54545....

Answer 1

Resposta:

1) 5/9

2) 33/99 → 1/3

3) 45/99 → 5/11

4) 4/9

5) 54/99 → 6/11

Answer 2

Explicação passo-a-passo:

0,555...=x(10)

5,555...=10x

10x-x=5,555...-0,555...

9x=5

x=5/9

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0,333...=x(10)

3,333...=10x

10x-x=3,333...-0,333...

9x=3

x=3/9(÷3)

x=1/3

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0,4545...=x(10)

4,5454...=10x(10)

45,4545...=100x

100x-x=45,4545...-0,4545...

99x=45

x=45/99(÷9)

x=5/11

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0,444...=x(10)

4,444...=10x

10x-x=4,444...-0,444...

9x=4

x=4/9

________________________________

0,5454...=x(10)

5,4545...=10x(10)

54,5454...=100x

100x-x=54,5454...-0,5454...

99x=54

x=54/99(÷9)

x=6/11