Question

Volte essa dizima periódica 0,2373737... em fração irredutível.

Answer 1

 0,2373737...=  237-2
                        990

 ==> 235
        990

Answer 2

$0,2373737...=0,2+0,0373737...\\0,2\overline{37}=0,2+(0,3737.../10)\\0,2\overline{37}=(2/10)+(0,3737.../10)\\0,2\overline{37}=(2+0,3737...)/10$

Trabalharemos em cima da dízima 0,37...:

$x = 0,3737...\\100*x=100*0,3737...\\100x=37,3737...\\100x=37+0,3737...\\100x=37+x\\100x-x=37\\x=37/99$
________________

$0,2\overline{37}=(2+0,3737...)/10\\0,2\overline{37}=(2+[37/99])/10\\0,2\overline{37}=([2*99+37]/99)/10\\0,2\overline{37}=(198+37)/(99*10)\\0,2\overline{37}=235/990\\0,2\overline{37}=47/198$