Question

Determine a fração geratriz das dízimas a seguir:

a-) 5,232323...
b-) 2,17...
c-) 1,263263...
d-) 4,297...

Answer 1

a)
5,232323... = 5 + 0,232323... = 5 + $\frac{23}{99}$ = $\frac{(99.5)+23}{99}$ = $\frac{495+23}{99}$ = $\frac{518}{99}$

b)
2,17... = 2 + 0,17... = 2 + $\frac{17}{99}$ = $\frac{(99.2)+17}{99}$ = $\frac{198+17}{99}$ = $\frac{215}{99}$

c)
1,263263263... = 1 + 0,263263263... = 1 + $\frac{263}{999}$ = $\frac{(999.1)+263}{999}$ = $\frac{999+263}{999}$ = $\frac{1262}{999}$

d)
4,297... = 4 + 0,297... = 4 + $\frac{297}{999}$ = $\frac{(999.4)+297}{999}$ = $\frac{3996+297}{999}$ = $\frac{4293}{999}$