0,(36)
[tex]0,(36)=x\\\\0,(36)=x|*100\\\\36,(36)=100x|-x\\\\36=99x\rightarrow x=\frac{36}{99}= \frac{4}{11}\\[/tex]
3,(72)
[tex]3,(72)=x\\\\3,(72)=x\ |*100\\\\372,(72)=100x\ |-x\\\\369=99x\rightarrow x=3\frac{8}{11}\\[/tex]
-6,(24)
[tex]-6,(24)=x\\\\-6,(24)=x\ |*100\\\\-624,(24)=100x\ |-x\\\\-618=99x\rightarrow x=-6\frac{8}{33}\\[/tex]
0,(9)
[tex]0,(9)=x\\\\0,(9)=x\ |*10\\\\9,(9)=10x\ |-x\\\\9=9x\rightarrow x=1\\[/tex]
41,7(9)
[tex]41,7(9)=x\\\\41,7(9)=x\ |*100\\\\4179,(9)=100x\\\\4179,(9)=100x\ |*10\\\\41799,(9)=1000x\\\\\left \{ {{4179,(9)=100x} \atop {41799,(9)=1000x}}\right.\\\\37620=900x\rightarrow x=41\frac{4}{5}\\[/tex]
2,1(52)
[tex]2,1(52)=x\\\\2,1(52)=x\ |*1000\\2152,(52)=1000x\\\\2152,(52)=1000x\ |*100\\215252,(52)=100000x\\\\\left \{{{2152,(52)=1000x}\atop {215252,(52)=100000x}} \right.\\\\213100=99000x\rightarrow x=2\frac{151}{990}\\[/tex]
