Reciprocal of 41
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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 --- ...
$\blacksquare$