Question

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

Answer 1

x=0,555...                           y=0,111....
10x=5,555...  x=5/9          10y=1,111...   y=1/9   a= 5/9 +1/9  a= 6/9=2/3

b=0,2 +0,24  b=0,44      b/a=  2/3/0,44   =50/33

Answer 2

$a = \\ 0,5555...= \frac{5}{9} \\ \\ 0,1111...= \frac{1}{9} \\ \\ a = \frac{5}{9} + \frac{1}{9} = \frac{6}{9} = \frac{2}{3} \\ \\ b = \\ 0,2 = \frac{2}{10} \\ \\ 0,04 = \frac{4}{100} \\ \\ b = \frac{2}{10}+ \frac{4}{100} = \frac{(20+4)}{100} = \frac{24}{100} \\ \\ \frac{b}{a} = \frac{ \frac{24}{100} }{ \frac{2}{3} } = \frac{24}{100} . \frac{3}{2}= \frac{72}{200} = \frac{36}{100} = \frac{9}{25}$

Espero ter ajudado.