Question

Помогите решить задание    

    2,(3)-1,(6)

------------------ х=2,(2)

0,1(3)+0,1(6)

Answer 1

$2.(3)=2+frac{0.3}{1-0.1}=2+frac{0.3}{0.9}=2+frac{1}{3}=frac{7}{3}$

 

$1.6=1+frac{0.6}{1-0.1}=1+frac{0.6}{0.9}=1+frac{2}{3}=frac{5}{3}$

 

$0.1(3)=0.1+frac{0.03}{1-0.1}=frac{1}{10}+frac{0.03}{0.9}=frac{1}{10}+frac{1}{30}=frac{4}{30}$

 

$0.1(6)=0.1+frac{0.06}{1-0.1}=frac{1}{10}+frac{0.06}{0.9}=frac{1}{10}+frac{2}{30}=frac{5}{30}$

 

$2.(2)=frac{2}{1-0.1}=frac{2}{0.9}=frac{20}{9}$

 

$frac{2.(3)-1.(6)}{0.1(3)+0.1(6)}=frac{frac{7}{3}-frac{5}{3}}{frac{4}{30}+frac{5}{30}}=frac{frac{2}{3}}{frac{9}{30}}=frac{2*30}{3*9}=frac{20}{9}$

 

$frac{20}{9}x=frac{20}{9}$

$x=1$