The repeating decimal \(0.5151....\) as a fully simplified fraction will be \(\frac{17}{33}\).
What is repeating decimal ?
Repeating decimal or recurring decimal is decimal representation of a number whose digits are periodic and the infinitely repeated portion is not zero.
We have,
Repeating decimal \(0.5151.....\) .
Let,
\(x=0.51\) \(..........(i)\)
As it have two decimal, so multiply on both sides by \(100\),
\(100x=51.51\) \(..........(ii)\)
Now, subtract equation \((i)\) from equation \((ii)\),
\(100x-x=51.51-0.51\)
\(99x=51\)
\(x=\frac{51}{99}\)
Now, to simplify it more divide numerator and denominator from \(3\),
We get ,
\(x=\frac{17}{33}\)
So, the simplified fraction of the given repeating decimal is \(\frac{17}{33}\).
Hence, we can say that the repeating decimal \(0.5151....\) as a fully simplified fraction will be \(\frac{17}{33}\).
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