Question

Ache a fração geratriz das dízimas a seguir:
a) 0,44444...
b)0,12525
c)0,54545
d)0,04777...
e)0,12343434....
f)0,23333...
g)0,15383383383383383..
h)0,024024
i)0,888313131...
j)0,32101230123...


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Answer 1

a) 0,444... = 4/9
b) 0,12525... = (125-1)/990 = 124/990
c) 0,54545... = 54/99 = (54:9)/(99:9) = 6/11
d) 0,04777... = (47-4)/900 = 43/900
e) 0,123434... = (1234-12)/9900 = 1232/9900 = 616/4950 = 308/2475
f) 0,2333... = (23-2)/90 = 21/90 = (21:3)/(90:3) = 7/30
g) 0,1538338338338... = (1538338 - 1538)/9990000 = 1536800/9990000 = 96050/624375
h) 0,024024... = 24/999 = (24:3)/(999:3) = 8/333
i) 0,8883131... = (88831-888)/99000 = 87943/99000
j) 0,32101230123... = (3210123-321)/9999000 = 3209802/9999000 = 1604901/4999500 = 534967/1666500