we write the decimal number as 1.282828... where the dots are indicating recurring decimals
let [tex]x=1.282828...[/tex]
and [tex]100x=128.282828...[/tex]
we choose to multiply [tex]x[/tex] by 100 in order to obtain a number that gives us same values after the decimal point
[tex]100x-x=128.282828...-1.282828...[/tex]
[tex]99x=127[/tex]
by subtracting [tex]x[/tex] from [tex]100x[/tex], we have an integer 127
rearranging to make [tex]x[/tex] the subject
[tex]99x=127[/tex]
[tex]x= \frac{127}{99} [/tex] is the rational number for 1.282828...
