Reciprocal of 451

Theorem

The decimal expansion of the reciprocal of $451$ is as follows:

$\dfrac 1 {451} = 0 \cdotp \dot 00221 \, 7294 \dot 9$

This sequence is A021455 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Proof

Performing the calculation using long division:

    0.0022172949002...
   -------------------
451)1.0000000000000
      902
      ---
       980
       902
       ---
        780
        451
        ---
        3290
        3157
        ----
         1330
          902
         ----
          4280
          4059
          ----
           2210
           1804
           ----
            4060
            4059
            ----
               1000
                902
               ----
               ....

$\blacksquare$

Also see

• Sequence of Smallest Numbers whose Reciprocal has Period n