The repeating decimal [tex]0.5151....[/tex] as a fully simplified fraction will be [tex]\frac{17}{33}[/tex].
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 [tex]0.5151.....[/tex] .
Let,
[tex]x=0.51[/tex] [tex]..........(i)[/tex]
As it have two decimal, so multiply on both sides by [tex]100[/tex],
[tex]100x=51.51[/tex] [tex]..........(ii)[/tex]
Now, subtract equation [tex](i)[/tex] from equation [tex](ii)[/tex],
[tex]100x-x=51.51-0.51[/tex]
[tex]99x=51[/tex]
[tex]x=\frac{51}{99}[/tex]
Now, to simplify it more divide numerator and denominator from [tex]3[/tex],
We get ,
[tex]x=\frac{17}{33}[/tex]
So, the simplified fraction of the given repeating decimal is [tex]\frac{17}{33}[/tex].
Hence, we can say that the repeating decimal [tex]0.5151....[/tex] as a fully simplified fraction will be [tex]\frac{17}{33}[/tex].
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