Question

DETERMINE o valor da expressão (0,666... - 1,2111...): 2,343434... :​

Answer 1

Resposta:

Explicação passo-a-passo:

Tenos que:

x = 0,666... (I)

10x = 6,666... (II)

Fazendo (II) - (I)

10x - x = 6,666... - 0,666...

9x = 6

x = 6/9

x = 2/3

y = 1,2111... (I)

10y = 12,111... (II)

100y = 121,111... (III)

Fazendo (III) - (II)

100y - 10y = 121,111... - 12,111...

90y = 109

y = 109/90

z = 2,343434... (I)

100z = 234,343434... (II)

Fazendo (II) - (I)

100z - z = 234,343434... - 2,343434...

99z = 232

z = 232/99

Assim:

(0,666... - 1,2111...): 2,343434... =

$(\frac{2}{3} - \frac{109}{90}):\frac{232}{99}=(\frac{30.2-109}{90}):\frac{232}{99}=(\frac{60-109}{90}):\frac{232}{99}=-\frac{49}{90}:\frac{232}{99}=-\frac{49}{90}.\frac{99}{232}=-\frac{49.11}{10.232}=-\frac{539}{2320}$