Question

convert 0.645bar into rational number

Answer 1

In rational no. it is
1/15

Answer 2

since,

let x be the number, that is 0.645645645....

so,

1000x = 645.645645645.....

then, let us substract 1000x from x.

1000x - x = 645.645645.... - 0.645645.....

=> 999x = 645

=> x = $\frac{645}{999}$

=> x = $\frac{215}{333}$ .....answer

thus,

0.645645645... in rational form = $\frac{215}{333}$