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Ta có :
\(0,0\left(8\right)=\dfrac{1}{10}.0,\left(8\right)=\dfrac{1}{10}.0,\left(1\right).8=\dfrac{1}{10}.\dfrac{1}{9}.8=\dfrac{4}{45}\)
\(0,1\left(2\right)=0,1+0,0\left(2\right)\)
\(=\dfrac{1}{10}+\dfrac{1}{10}.0,\left(2\right)=\dfrac{1}{10}+\dfrac{1}{10}.0,\left(1\right).2\)
\(=\dfrac{1}{10}+\dfrac{1}{10}.\dfrac{1}{9}.2=\dfrac{9}{90}+\dfrac{2}{90}=\dfrac{11}{90}\)
\(0,1\left(23\right)=0,1+0,0\left(23\right)=\dfrac{1}{10}+\dfrac{1}{10}.0,23\)
\(=\dfrac{1}{10}+\dfrac{1}{10}.0,\left(01\right).23\)
\(\dfrac{1}{10}+\dfrac{1}{10}.\dfrac{1}{99}.23=\dfrac{99}{990}+\dfrac{23}{990}=\dfrac{122}{990}=\dfrac{61}{495}\)
1) b) \(0,555..=0,\left(5\right)=\frac{5}{9}\)
a) 0,555=\(\frac{555}{1000}=\frac{111}{200}\)
c) \(0,25454..=0,2\left(54\right)=\frac{14}{55}\)
2) a) \(1,\left(6\right).2,\left(3\right):0,\left(7\right)=\frac{5}{3}.\frac{7}{3}:\frac{7}{9}=\frac{35}{9}:\frac{7}{9}=5\)
b) \(0,\left(37\right)+0,\left(62\right)=\frac{37}{99}+\frac{62}{99}=1\)
c) \(0,\left(33\right).3=\frac{1}{3}.3=1\)
Bài 1:
\(0,0\left(8\right)=\frac{1}{10}\cdot0,\left(8\right)=\frac{1}{10}\cdot0,\left(1\right)\cdot8=\frac{4}{5}\cdot\frac{1}{9}=\frac{4}{45}\)
\(0,1\left(2\right)=0,1+0,0\left(2\right)=\frac{1}{10}+\frac{1}{10}\cdot0,\left(2\right)=\frac{1}{10}+\frac{1}{10}\cdot0,\left(1\right)\cdot2=\frac{1}{10}+\frac{1}{5}\cdot\frac{1}{9}=\frac{1}{10}+\frac{1}{45}=\frac{11}{90}\)
\(0,1\left(23\right)=0,1+0,\left(23\right)=\frac{1}{10}+0,\left(01\right)\cdot23=\frac{1}{10}+\frac{1}{99}\cdot23=\frac{1}{10}+\frac{23}{99}=\frac{329}{990}\)