Question

Determine as frações geratrizes das racionais.

a) 0,222... d) 0,1212...

b) 0,321321... e) 0,333...

c) 0,34545... f) 0,23131...

Answer 1

$a) \ 0,222...=\frac{2}{9}\\ b) \ 0,321321...=\frac{321}{999}=\frac{107}{333}\\ c) \ 0,34545...=\frac{3,454545...}{10}=\frac{3+\frac{45}{99}}{10}=\frac{\frac{38}{11}}{10}=\frac{38}{110}\\ \\ d) \ 0,121212...=\frac{12}{99}\\ \\ e) \ 0,333...=\frac{3}{9}=\frac{1}{3}\\ \\ f) \ 0,23131...=\frac{2,3131...}{10}=\frac{2+\frac{31}{99}}{10}=\frac{\frac{229}{99}}{10}=\frac{229}{990}$