What is 0.20833333333 simplified?

The easiest way to solve this kind of problem is to muliply the number so that all the digits that are NOT part of the recurring portion are to the left of the decimal point.

In this case we multiply by 1000 so that the 0.208 becomes 208.

Also, let the original number be represented by a.

0.2083 (3 recurring) x 1000 = 208.3 (3 recurring) = 1000a

Now subtract the original number :

1000a - a = 999a = 208.3 (3 recurring) - 0.2083 (3 recurring) = 208.125

Then, a = 208.125/999

If this is expanded to become 208125/999000 then it simplifies to 5/24.