Question

Se x e y são racionais e x = 0,1010101010...
y = 0,0101010101..., indentifique a alternativa que representa o quociente x/y.
a)0,0101010101...
b)0,11
c)10
d)10,10101010...
e)11

Answer 1

$x = 0,101010... = \frac{10}{99}\\y=0,0101010... = \frac{10}{990} = \frac{1}{99}\\\\ \frac{x}{y}= \frac{ \frac{10}{99}}{ \frac{1}{99}}=\frac{10}{99}.\frac{99}{1}=10$