Question

qual são a fracão geratriz de A) 3,111... B) 0,7222... C)5,0333... D)1,34444...

Answer 1

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Ola Cristofer 

A) 

3.111.. = 3 + 0.111..

x = 0.111
10x = 1.111..

9x = 1

x = 1/9 

3 + 1/9 = 28/9 

3.111... = 28/9 

B) 

0.7222..  = 7/10 + 0.0222... 

x = 0.0222...

100x = 2.222...
10x = 0.222...

90x = 2

x = 1/45 

7/10 +  1/45 = (7*45 + 10)/450 = 13/18 

0.7222... = 13/18 

C) 

5.0333.. = 5 + 0.0333

x = 0.0333..

1000x = 33.333...
100x = 3.333...

900x = 30

x = 30/900 = 1/30 

5.0333... = 5 + 1/30 = 151/30 

D) 

1.3444... = 1 + 3/10 + 0.0444...

x = 0.0444..

1000x = 44.444...
100x = 4.44

900x = 40

x = 40/900 = 4/90 

1 + 3/10 + 4/90 = 90/90 + 27/90 + 4/90 = 121/90 

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