Question

determine a fração geratriz de cada dízima periódica
a-)0,1111...
b-)9,020202...
c-)5,001001001001001...
d-)7,34343434...
e-)3,54444...​

Answer 1

a) 0,1111... = 0,1 = $\frac{1-0}{9} = \frac{1}{9}$

b) 9,020202... = 9,02 = $\frac{902 - 9}{99}$ $=\frac{893}{99}$

c) 5,001001001001001... = 5,001 = $\frac{5001-5}{999} = \frac{4996}{999}$

d) 7,34343434... = 7,34 = $\frac{734-7}{99} = \frac{727}{99}$

e) 3,54444...​ = 3,54 = $\frac{354-35}{90} = \frac{319}{90}$