Problema 25

$$1,8\cdot \frac{1,\bar 9 \cdot 0,\bar 9}{0,0\bar 9}=$$

a) 18

b) 36

c) 0,36

d) $$\left( \frac{18}{10} \right)$$

e) 1,8


SOLUCIÓN:

Trasformamos los decimales a fracción:

$$1,8=\frac{18}{10}=\frac{9}{5}$$

$$1,\bar 9 = \frac{19-1}{9}=\frac{18}{9}=2$$

$$0,\bar 9 = \frac{9-0}{9}=1$$

$$0,0\bar 9 = \frac{9-0}{90}=\frac{1}{10}$$


Entonces, se sigue:

$$1,8\cdot \frac{1,\bar 9 \cdot 0,\bar 9}{0,00\bar 9}=\frac{9}{5}\cdot \frac{2\cdot1}{\frac{1}{10}}=\frac{9}{5}\cdot \left( 2 : \frac{1}{10} \right) = \frac{9}{5}\cdot \left( 2 \cdot 10 \right) = $$

$$=\frac{9}{5} \cdot 20 = 9\cdot 4 = 36$$