Question

determine a fraçao geratriz cada uma das dizima abaixo
A-0,888
B-3,1515
C-0,05222
D-0,00700700
E-2,4777
F-0,1444

Answer 1

a-0,888..
x=0,888...
10x=8,888...
10x-x=8,888...-0,888...
9x=8
x=8/9

b-3,1515..
x=3,1515..
100x=315,1515..
100x-x=315,1515..-3,1515..
99x=312
x=312/99
x=104/33

c-0,05222...
x=0,05222...
100x=5,222...
1000x=52,222...
1000x-100x=52,222-5,222
900x=47
x=47/900

d-0,00700700
x=0,00700700
100000x=700,700700...
100000000x=700700,700700...
100000000x-100000x=700700,700700...-700,700700...
99900000x=700000
x=700000/99900000
x=7/999

e-2,4777...
x=2,477...
100x=247,777... 
1000x=2747,777...
1000x-100x=2477,777-247,777
900x=2230
x=2230/900
x=223/90

f-0,1444...

x=0,1444...
10x=1,4444...
100x=14,444...
100x-10x=14,444...-1,444..
90x=13
x=13/90