Reciprocal of 3
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Theorem
The decimal expansion of the reciprocal of $3$ is as follows:
- $\dfrac 1 3 = 0 \cdotp \dot 3$
This sequence is A010701 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Proof
Performing the calculation using long division:
0.33... -------- 3)1.00... 9 --- 10 9 -- ..
$\blacksquare$