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: \(0,\left(12\right)=12\times0,\left(01\right)=12\times\frac{1}{99}=\frac{4}{33}\)

\(1,\left(6\right)=1+6\times0,\left(1\right)=1+6\times\frac{1}{9}=\frac{5}{3}\)

\(0,\left(4\right)=4\times0,\left(1\right)=4\times\frac{1}{9}=\frac{4}{9}\)

\(\Rightarrow\frac{4}{33}\div\frac{5}{3}=x\div\frac{4}{9}\Rightarrow x\div\frac{4}{9}=\frac{4}{55}\Rightarrow x=\frac{4}{55}\times\frac{4}{9}\Rightarrow x=\frac{16}{495}\)

16/495

chuẩn rồi 16/495

Bài làm:

Ta có: \(10,\left(3\right)+0,\left(4\right)-8,\left(6\right)\)

\(=\frac{31}{3}+\frac{4}{9}-\frac{26}{3}\)

\(=\frac{93+4-78}{9}\)

\(=\frac{19}{9}\)

Ta có : 12,(1) = 12 + 0,(1) = 12 + \(\dfrac{1}{9}\)=\(\dfrac{109}{9}\)

2,3(6) = 2,3 + \(\dfrac{1}{10}.0,\left(6\right)=2,3+\dfrac{1}{10}.6.0,\left(1\right)=2,3+\dfrac{1}{10}.6.\dfrac{1}{9}=\dfrac{71}{30}\)

4,(21)=4+21.0,(01)=4+21.\(\dfrac{1}{99}=\dfrac{139}{33}\)

\(\Rightarrow\left[\dfrac{109}{9}-\dfrac{71}{30}\right]:\dfrac{139}{33}=\dfrac{9647}{4170}\)

=(109/9-71/30):139/33

=877/90*33/139

\(\simeq2,31\)