Question

Encontre a fração geratriz de cada dízima periódica e dos decimais exatos.

a) 1,8181...
b)1,354354...
c)0,213434...
d)0,12525...

Answer 1

A.
x = 1,8181...
100x = 181,8181...
99x = 180
x = $\frac{180}{99}$
B.
x = 1,354354...
1000x = 1354,35435...
999x = 1353
x = $\frac{1353}{999}$ 
C.
x = 0,213434...
10000x = 21,3434...
100x = 21,3434...
9900x = 2113
x = $\frac{2113}{9900}$
D.
x = 0,12525...
1000x = 125,2525...
10x = 1,2525...
990x = 124
x = $\frac{124}{990}$