Question

Tính: \(0,1\left(2\right)\) và \(0,1\left(23\right)\)

Answer 1

\(0,1\left(2\right)=0,1+0,0\left(2\right)=\frac{1}{10}+\frac{0,\left(2\right)}{10}\)

           \(=\frac{1}{10}+\frac{0,\left(1\right).2}{10}=\frac{1}{10}+\frac{\frac{1}{9}.2}{10}\)

           \(=\frac{1}{10}+\frac{\frac{2}{9}}{10}=\frac{11}{9}.\frac{1}{10}=\frac{11}{90}\)

\(0,1\left(23\right)=0,1+0,0\left(23\right)=\frac{1}{10}+\frac{0,\left(23\right)}{10}\)

             \(=\frac{1}{10}+\frac{0,\left(01\right).23}{10}=\frac{1}{10}+\frac{\frac{1}{99}.23}{10}\)

             \(=\frac{1}{10}+\frac{\frac{23}{99}}{10}=\frac{122}{99}.\frac{1}{10}=\frac{61}{495}\)