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0.2 recurring as a fraction?

Guest Feb 16, 2017
 #1
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0.222222222222....=2/9

Guest Feb 16, 2017
 #2
avatar+19597 
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0.2 recurring as a fraction?

 

\(\begin{array}{|rcll|} \hline 10\cdot 0.\bar{2} &=& 2.\bar{2} \\ 1\cdot 0.\bar{2} &=& 0.\bar{2} \\\\ 10\cdot 0.\bar{2} - 1\cdot 0.\bar{2} &=& 2.\bar{2}-0.\bar{2} \\ 9\cdot 0.\bar{2} &=& 2 \\ 0.\bar{2} &=& \frac{2}{9} \\ \mathbf{ 0.2\ recurring } &\mathbf{=}& \mathbf{ \frac{2}{9} }\\ \hline \end{array} \)

 

laugh

heureka  Feb 16, 2017
edited by heureka  Feb 16, 2017

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