将无限循环小数2. ...化为分数

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2.232323....=2+0.23+0.0023+0.000023+....将0.23+0.0023+0.000023+....看成是一个无穷等比数列求和,q=0.0023/0.23=0.01所以2.232323....=2+0.23+0.0023+0.000023+....=2+0.23/(1-0.01)=2+23/99=221/99