From decimal to fraction
We want to change
[tex]\bar{.83}[/tex]
to a fraction.
This is
0.8383838383.... into a fraction
If we multiply 0.8383.. by 100, the decimal would be located two digits to the right:
100 x 0.8383.. = 83.8383...
Then,
If we substract both sides of the equations:
Then, we have that:
[tex]\begin{gathered} 99\times0.8383\ldots=83 \\ 99\times0.\bar{83}=83 \end{gathered}[/tex]
Taking 99 to the right:
[tex]\begin{gathered} 99\times0.\bar{83}=83 \\ 0.\bar{83}=\frac{83}{99} \end{gathered}[/tex]
Answer: 83/99
