Since the line is over the numbers 6 and 4, then there are 2 repeating digits, that is:
[tex]0.\bar{64}=0.64646464\ldots[/tex]
Now, create an equation such that x equals the decimal number:
[tex]\begin{gathered} x=0.\bar{64} \\ x=0.6464\ldots\Rightarrow\text{ Equation 1} \end{gathered}[/tex]
Since 2 figures are repeated then multiply by 100 on both sides of the equation:
[tex]\begin{gathered} 100\cdot x=0.\bar{64}\cdot100 \\ 100x=64.6464\ldots\Rightarrow\text{ Equation 2} \end{gathered}[/tex]
Now subtract equation 1 from equation 2:
[tex]\begin{gathered} 100x=64.6464 \\ x=0.6464\text{ -} \\ ---------- \\ 99x=64 \end{gathered}[/tex]
Finally, solve for x
[tex]\begin{gathered} 99x=64 \\ \text{ Divide by 99 into both sides of the equation} \\ \frac{99x}{99}=\frac{64}{99} \\ x=\frac{64}{99} \end{gathered}[/tex]
Therefore, the fraction that represents 0.64 is
[tex]\frac{64}{99}[/tex]
