1)Ta có: \(12,\left(1\right)=12+0,\left(1\right)=12+\frac{1}{9}=\frac{109}{9}\);
\(2,3\left(6\right)=2,3+\frac{1}{10}\times0,\left(6\right)=2,3+\frac{1}{10}\times6\times0,\left(1\right)=2,3+\frac{1}{10}\times6\times\frac{1}{9}=\frac{71}{30}\)\(4,\left(21\right)=4+21\times0,\left(01\right)=4+21\times\frac{1}{99}=\frac{139}{33}\)
\(\Rightarrow\)\(\left[\frac{109}{9}-\frac{71}{30}\right]\div\frac{139}{33}=\frac{9647}{4170}\)
2)Ta có: \(0,\left(12\right)=12\times0,\left(01\right)=12\times\frac{1}{99}=\frac{4}{33}\)
\(1,\left(6\right)=1+6\times0,\left(1\right)=1+6\times\frac{1}{9}=\frac{5}{3}\)
\(0,\left(4\right)=4\times0,\left(1\right)=4\times\frac{1}{9}=\frac{4}{9}\)
\(\Rightarrow\frac{4}{33}\div\frac{5}{3}=x\div\frac{4}{9}\Rightarrow x\div\frac{4}{9}=\frac{4}{55}\Rightarrow x=\frac{4}{55}\times\frac{4}{9}\Rightarrow x=\frac{16}{495}\)
