What is the rational number equivalent to 1 point 28 with a bar over 28

We write the decimal number as 1.282828... where the dots are indicating recurring decimals

let 
and 

we choose to multiply  by 100 in order to obtain a number that gives us same values after the decimal point




by subtracting  from , we have an integer 127

rearranging to make  the subject


is the rational number for 1.282828...