Let
[tex]x=0.2464646..[/tex]
Multiply x by a power of [tex]10[/tex], one that keeps the decimal part of the number the same:
[tex]\\1,000x=246.4646..[/tex]
[tex]\\10x=2.464646..[/tex]
Subtract [tex]\\10x[/tex] from [tex]\\1000x[/tex]
[tex]\\1,000x-10x=246.4646..-2.464646..=244[/tex]
The repeating decimals should cancel out
[tex]\\990x=244[/tex]
solve for x
Divide by [tex]990[/tex] both sides
[tex]990x/990=244/990[/tex]
[tex]x=244/990[/tex]
Simplify
Divide by [tex]2[/tex] both numerator and denominator
[tex]x=122/495[/tex]
therefore
the answer is
The fraction in simplest form is [tex]122/495[/tex]
