Reciprocal of 99

Theorem

The decimal expansion of the reciprocal of $99$ is:

$\dfrac 1 {99} = 0 \cdotp \dot 0 \dot 1$

This sequence is A000035 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Proof

Performing the calculation using long division:

   0.0101...
  ----------
99)1.0000000
     99
     --
      100
       99
      ---
      ...

$\blacksquare$

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $99$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $99$