Question

I need help solving a repeated math equation the top is 83 but the bottom is not 100

Answer 1

From decimal to fraction

We want to change

`\bar{.83}`

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:

`\begin{gathered} 99*0.8383\ldots=83 \\ 99*0.\bar{83}=83 \end{gathered}`

Taking 99 to the right:

`\begin{gathered} 99*0.\bar{83}=83 \\ 0.\bar{83}=(83)/(99) \end{gathered}`

Answer: 83/99