Question

Como obter frações geratrizes das dizimas periódicas: 0,777...,0444... ,0,18, 2,333... 1,5, 2,35, 0,02, 1,235

Answer 1

0,7777....

x = 0,7777...
10x = 7,77777...
10x = 7 + 0,77777...
10x = 7 + x
10x - x = 7

9x = 7
x = 7/9

0,7777... = 7/9
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0,44444...

x = 0,44444....
10x = 4,444444...
10x = 4 + 0,444444...
10x = 4 + x
10x - x = 4
9x = 4

x = 4/9

0,4444... = 4/9
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0,18

x = 0,18
100x = 18
x = 18/100
x = 18:/100/2

x = 9/50

0,18 = 9/50
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2,33333...
2 + 0,3333333...

x = 0,333333...
10x = 3,3333333...
10x = 3 + 0,3333333...
10x = 3 + x
9x = 3
x = 3/9
x = 3:3/9:3

x = 1/3

2,3333... = 2 + 1/3
2,3333... = (6+1)/3
2,3333... = 7/3

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1,5

x = 1,5
10x = 15
x = 15/10
x = 15:5/10:5
x = 3/2

1,5 = 3/2
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2,35

x = 2,35
100x = 235
x = 235/100
x = 235:5/100:5

x = 47/20

2,35 = 47/20

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0,02

x = 0,02

100x = 2

x = 2/100

x = 2:2/100:2
x = 1/50

0,02 = 1/50
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1,235

x = 1,235
1000x = 1235
x = 1235/1000

x = 1235:5/1000:5

x = 247/200

1,235 = 247/200