Reciprocal of 41

Theorem

The decimal expansion of the reciprocal of $41$ is as follows:

$\dfrac 1 {41} = 0 \cdotp \dot 0243 \dot 9$

This sequence is A021045 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Proof

Performing the calculation using long division:

   0.0243902...
  -------------
41)1.0000000...
     82           
   ----   
     180
     164
     ---
      160
      123
      ---
       370
       369
       ---
         100
          82
         ---
         ...

$\blacksquare$