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