Question

Se x = 0,3232... e y = 0,1626262..., então x - y é igual a

Answer 1

$\boxed{\begin{array}{l}\sf x=0,323232... \cdot100\\\sf 100x=32,323232...\\-\underline{\begin{cases}\sf100x=32,323232...\\\sf x=0,323232... \end{cases}}\\\sf 99x=32\\\sf x=\dfrac{32}{99}\\\sf y=0,1626262...\cdot10\\\sf 10y=1,626262...\cdot10\\\sf100y=162,626262...\\-\underline{\begin{cases}\sf100y=162,626262...\\\sf10y=1,626262...\end{cases}}\\\sf90y=161\\\sf y=\dfrac{161}{90}\\\sf x-y=\dfrac{32}{99}-\dfrac{161}{90}=\dfrac{320-1771}{990}=-\dfrac{1451}{990}\end{array}}$