The solution is as follows;

You have number 0.833333.... This number is equal to some fraction; call this fraction "x". That is:

X = 0.833333...

There is one repeating digit in this decimal, so multiply x by "1" followed by one zero; that is, multiply by 10:

10x = 8.33333....

Now subtract the former from the latter:

10x=8.33333

x = 0.833333

------

9x = 7.50000

That is, 9x = 7.5 = 75/10 = 15/2. Solving this, we get x = 15/18. (You can verify this by plugging "15 รท 18" into your calculator and seeing that you get "0.833333..." for an answer.)

You have number 0.833333.... This number is equal to some fraction; call this fraction "x". That is:

X = 0.833333...

There is one repeating digit in this decimal, so multiply x by "1" followed by one zero; that is, multiply by 10:

10x = 8.33333....

Now subtract the former from the latter:

10x=8.33333

x = 0.833333

------

9x = 7.50000

That is, 9x = 7.5 = 75/10 = 15/2. Solving this, we get x = 15/18. (You can verify this by plugging "15 รท 18" into your calculator and seeing that you get "0.833333..." for an answer.)