Reciprocal of 239

Theorem

The decimal expansion of the reciprocal of $239$ is as follows:

$\dfrac 1 {239} = 0 \cdotp \dot 00418 \, 4 \dot 1$

This sequence is A021243 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Proof

Performing the calculation using long division:

    0.0041841004...
   -------------
239)1.0000000000...
      956           
     ----   
       440
       239
       ---
       2010
       1912
       ----
         980
         956
         ---
          240
          239
          ---
            1000
             956
            ----
             ...

$\blacksquare$