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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: \(0,\left(12\right)=12\times0,\left(01\right)=12\times\frac{1}{99}=\frac{4}{33}\)
\(1,\left(6\right)=1+6\times0,\left(1\right)=1+6\times\frac{1}{9}=\frac{5}{3}\)
\(0,\left(4\right)=4\times0,\left(1\right)=4\times\frac{1}{9}=\frac{4}{9}\)
\(\Rightarrow\frac{4}{33}\div\frac{5}{3}=x\div\frac{4}{9}\Rightarrow x\div\frac{4}{9}=\frac{4}{55}\Rightarrow x=\frac{4}{55}\times\frac{4}{9}\Rightarrow x=\frac{16}{495}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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.\(\dfrac{1}{99}=\dfrac{139}{33}\)
\(\Rightarrow\left[\dfrac{109}{9}-\dfrac{71}{30}\right]:\dfrac{139}{33}=\dfrac{9647}{4170}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left[12.\left(1\right)-2.3\left(6\right)\right]:4.\left(21\right)\)
\(=\left[\dfrac{109}{9}-\dfrac{71}{30}\right]:\dfrac{139}{33}\)
\(=\dfrac{877}{90}\cdot\dfrac{33}{139}\simeq2.313\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài làm:
Ta có: \(10,\left(3\right)+0,\left(4\right)-8,\left(6\right)\)
\(=\frac{31}{3}+\frac{4}{9}-\frac{26}{3}\)
\(=\frac{93+4-78}{9}\)
\(=\frac{19}{9}\)