Question

So sánh

0.(31) và 0.3(13)

Answer 1

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) = \(\frac{310}{99}:10=\frac{31}{99}\)