Question

 Sendo a = 0,555... + 0,111...  e  b = 0,2 + 0,04, determine o valor do quociente : b/a

Answer 1

a:
0.5555...=5/9;
0.1111...=1/9;
5/9+1/9=6/9.

b:
0.2=2/10;
0.04=4/100;
2/10+4/100=20/100+4/100=24/100;

$\frac{b= \frac{24}{100}}{a= \frac{6}{9} } = \frac{24}{100}*\frac{9}{6} = \frac{216}{600} = 0.36$