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Determinați cifra x știind că: 0,34(x)=[tex] \frac{26}{75} [/tex]

Răspuns :

 [tex]0,34(x)=\frac{\overline{34x}-34}{900}\;;\\
\Rightarrow\;\frac{\overline{34x}-34}{900}=\frac{26}{75}\;\Leftrightarrow\;75\cdot(\overline{34x}-34)=26\cdot900[/tex]
75*(340+x-34)=26*900
25500+75x-2550=23400
75x=23400-22950
75x=450
x=6