Question

determine as frações que geram os dízimas abaixo
a) 6,22222...
b) 0,33333...
c) 6,01010101...
d)7,2414141...
e) 1,712712712 ...

Answer 1

a) 6,22... = 6 + 0,22... = 6 + 2/9 = 56/9.
b) 0,33... = 3/9 = 1/3.
c) 6,0101... = x | 60,1010... = 10x | 60 + 10/99 = 10x | (5940 + 10)/99 = 10x | x = 595/99.
d) 7,241414... = x | 724,1414... = 100x | 724 + 0,1414... = 100x | 724 + 14/99 = 100x | 100x = (71676 + 14)/99 | x = 7169/990.
e) 1,712727... = x | 17,127127... = 10x | 17 + 127/999 = 10x | 17110/999 = 10x | x = 1711/999