Reciprocal of 17
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Theorem
The decimal expansion of the reciprocal of $17$ is as follows:
- $\dfrac 1 {17} = 0 \cdotp \dot 05882 \, 35294 \, 11764 \, \dot 7$
This sequence is A007450 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Proof
Performing the calculation using long division:
0.058823529411764705... ------------------------ 17)1.000000000000000000000 85 68 -- -- 150 20 136 17 --- -- 140 30 136 17 --- -- 40 130 34 119 -- --- 60 110 51 102 -- --- 90 80 85 68 -- -- 50 120 34 119 -- --- 160 100 153 85 --- --- 70 ... 68
$\blacksquare$