Reciprocal of 29
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Theorem
The decimal expansion of the reciprocal of $29$ is as follows:
- $\dfrac 1 {29} = 0 \cdotp \dot 03448 \, 27586 \, 20689 \, 65517 \, 24137 \, 93 \dot 1$
This sequence is A021033 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Proof
Performing the calculation using long division:
0.034482758620689655172413793103... ------------------------------------ 29)1.000000000000000000000000000000... 87 -- 130 180 150 230 116 174 145 203 --- --- --- --- 140 60 50 270 116 58 29 261 --- -- -- --- 240 200 210 90 232 174 203 87 --- --- --- -- 80 260 70 30 58 232 58 29 -- --- -- -- 220 280 120 100 203 261 116 87 -- --- --- --- 170 190 40 ... 145 174 29 --- --- -- 250 160 110 232 145 87 --- --- --- 180 150 230
$\blacksquare$