Question

Encontre a fração geratriz das dízimas periódicas:
**** __ *******_ *****__ ******_
a)0,1 2 b)0,1 2 c)2,1 7 d)2,1 7

Answer 1

a) x= 0,12...
100x = 12,12...
 
100x-x=12,12...- 0,12...
99x = 12
x = 12: 99
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b) x= 0,1222...
10x= 1,2...

10x-x = 1,2... - 0,122...
9x = 1,1
x= 11:90
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c) x= 2,17...
100x= 217,17...

100x-x= 217,17... - 2,17...
99x= 215
x= 215: 99
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d) x= 2,177...
10x = 21,7...

10x-x=21,77... - 2,17...
9x = 19,6
x= 196:90