represente cada dígima periódica na forma de fração irredutível
a) 0,212121...
b) 3,111...
c) 4,222...
d) 1,333...
e) 2,0111...
f) 5,222...
g) 8,111..
h) 2,050505...
i) 6,333...
j) 1,545454...
a) 0,212121...
b) 3,111...
c) 4,222...
d) 1,333...
e) 2,0111...
f) 5,222...
g) 8,111..
h) 2,050505...
i) 6,333...
j) 1,545454...
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Resposta:
a) 0,212121... = 212121... / 1000000... = 21 / 100 + 21 / 10000 + 21 / 1000000 + ... = 21/100 + 7/2500 + 7/100000 + ...
b) 3,111... = 111... / 100 + 111... / 1000 + 111... / 10000 + ... = 111/100 + 111/1000 + 111/10000 + ...
c) 4,222... = 222... / 100 + 222... / 1000 + 222... / 10000 + ... = 222/100 + 222/1000 + 222/10000 + ...
d) 1,333... = 333... / 1000 + 333... / 10000 + 333... / 100000 + ... = 333/1000 + 333/10000 + 333/100000 + ...
e) 2,0111... = 0111... / 100 + 111... / 10000 + 111... / 1000000 + ... = 11/100 + 11/10000 + 11/1000000 + ...
f) 5,222... = 222... / 100 + 222... / 1000 + 222... / 10000 + ... = 222/100 + 222/1000 + 222/10000 + ...
g) 8,111.. = 111... / 100 + 111... / 1000 + 111... / 10000 + ... = 111/100 + 111/1000 + 111/10000 + ...
h) 2,050505... = 050505... / 10000 + 50505... / 1000000 + ... = 505 / 10000 + 505 / 1000000 + ...
i) 6,333... = 333... / 100 + 333... / 1000 + 333... / 10000 + ... = 333/100 + 333/1000 + 333/10000 + ...
j) 1,545454... = 545454... / 100000 + 45454... / 1000000 + ... = 5454 / 100000 + 454 / 1000000 + ...