Reciprocal of 27
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Theorem
The decimal expansion of the reciprocal of $27$ is as follows:
- $\dfrac 1 {27} = 0 \cdotp \dot 03 \dot 7$
This sequence is A021027 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Proof
Performing the calculation using long division:
0.037... -------- 27)1.00000 81 -- 190 189 --- 100 81 --- ...
It is to be noted that this is because $999 = 27 \times 37$.
$\blacksquare$