Question

Encontre a fração geratriz de cada dízima periódica e dos decimais exatos.
a)0,444...
b) 1,8181...
c)1,354354...
d)0,213434...
e)0,12525...

Answer 1

A.
X = 0,444...
10x = 4,444...
9x = 4
x = $\frac{4}{9}$
B.
x = 1,8181...
100x = 181,8181...
99x = 180
x = $\frac{180}{99}$
C.
x = 1,354354...
1000x = 1354,35435...
999x = 1353
x = $\frac{1353}{999}$
D.
x = 0,213434...
10000x = 21,3434...
100x = 21,3434...
9900x = 2113
x = $\frac{2113}{9990}$
E.
x = 0,12525...
1000x = 125,2525...
10x = 1,2525...
990x = 124
x = $\frac{124}{990}$