Respuesta :

WojtekR
1.

[tex]0.\overline{36}=0.36363636\ldots[/tex]

Let:

[tex]x=0.363636\ldots\quad|\cdot100\\\\100x=36.363636\ldots\\\\100x=36+0.363636\ldots\\\\100x=36+x\quad|-x\\\\100x-x=36+x-x\\\\99x=36\quad|:99\\\\\\x=\dfrac{36}{99}\\\\\\\boxed{x=\frac{4}{11}} [/tex]

2.

[tex]0.3\overline{6}=0.366666\ldots\quad|\cdot10\\\\10\cdot0.3\overline{6}=3.66666\ldots[/tex]

Let:

[tex]x=0.66666\ldots\quad|\cdot10\\\\10x=6.66666\ldots\\\\10x=6+0.66666\ldots\\\\10x=6+x\quad|-x\\\\10x-x=6+x-x\\\\9x=6\quad|:9\\\\\\x=\dfrac{6}{9}=\dfrac{2}{3}[/tex]

so:

[tex]10\cdot0.3\overline{6}=3.66666\ldots\\\\10\cdot0.3\overline{6}=3+0.66666\ldots\\\\10\cdot0.3\overline{6}=3+x\\\\\\10\cdot0.3\overline{6}=3+\dfrac{2}{3}\\\\\\10\cdot0.3\overline{6}=\dfrac{9}{3}+\dfrac{2}{3}\\\\\\10\cdot0.3\overline{6}=\dfrac{11}{3}\qquad|:10\\\\\\\boxed{0.3\overline{6}=\dfrac{11}{30}} [/tex]

3. From definition:

[tex]0.36=\dfrac{36}{100}=\boxed{\dfrac{9}{25}}[/tex]

Answer:

36/99

Step-by-step explanation:

36/99

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