Reciprocal of 31
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Theorem
The decimal expansion of the reciprocal of $31$ is as follows:
- $\dfrac 1 {31} = 0 \cdotp \dot 03225 \, 80645 \, 1612 \dot 9$
This sequence is A021035 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Proof
Performing the calculation using long division:
0.03225806451612903... ----------------------- 31)1.00000000000000000000 93 155 -- --- 70 50 62 31 -- -- 80 190 62 186 -- --- 180 40 155 31 --- -- 250 90 248 62 --- -- 200 280 186 279 --- --- 140 100 124 93 --- --- 160 ... 155 ---
$\blacksquare$