The fraction that represents the repeating decimal is
[tex]\frac{479}{1100}[/tex]
Given :
A repeating decimal [tex]0.4354545454...............[/tex]
there is bar at 54 , so 54 is repeating
We need to convert this decimal into fraction
54 is repeating so we multiply by 100
Let x= [tex]0.4354545454...............\\[/tex]
[tex]100x=43.54545454...............[/tex]
Now we subtract x from 100x
[tex]100x=43.54545454...............\\ x= 0.4354545454...............\\-----------------------------------------\\ 99x=43.11[/tex]
Now divide both side by 99
[tex]x=\frac{43.11}{99} \\[/tex]
multiply top and bottom by 100 to remove the decimal
[tex]x=\frac{4311}{9900} \\Divide \; top \; and \; bottom \; by 9\\x=\frac{479}{1100}[/tex]
Learn more :
brainly.com/question/15666599
