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![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: \(0,\left(01\right)=\frac{1}{99}\)
=> \(0,\left(31\right)=0,\left(01\right)\times31=\frac{1}{99}\times31=\frac{31}{99}\)
Ta có: 10 x 0,3(13) = 3,(13) = 3+0(13)
Mà \(0,\left(13\right)=0,\left(01\right)\times13=\frac{1}{99}\times13=\frac{13}{99}\)
=> 10 x 0,3(13) = \(3+\frac{13}{99}=\frac{310}{99}\)
=> 0,3(13) = \(\frac{310}{99}:10=\frac{31}{99}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a ) 0,(31)+ 0,3(13) . 0, (52) = 0
b ) 2,1(34) . 0,3 - 3,1(25) = -56,08
![](https://rs.olm.vn/images/avt/0.png?1311)
0,(31)=0,313131...
0,3(13)=0,313131...
vậy 0,(31) = 0,3(13)
\(0,\left(31\right)=\frac{31}{99}\)
\(0,3\left(13\right)=\frac{313-3}{990}=\frac{310}{990}=\frac{31}{99}\)
Vậy.......
![](https://rs.olm.vn/images/avt/0.png?1311)
\(0.\left(31\right)=\dfrac{31}{99}\)
\(0.3\left(13\right)=\dfrac{31}{99}\)
Do đó: 0,(31)=0,3(13)
![](https://rs.olm.vn/images/avt/0.png?1311)
*0,(31)=0,(01)*31=1/99*31=31/99
* 0,3(13) =0,3 +0,0(13) =0,3+1/10 *0,(13)=3/10+1/10 *0,(01)*13
=3/10+1/10 *1/99*13=310/990 =31/99
vậy 0,(31) = 0,3(13)
0,(31) = 0,3(13)
0,(31)=0,3(13)
0,31=0,3100>0,3(13)=0,3131313