Reciprocal of 47
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Theorem
The decimal expansion of the reciprocal of $47$ is as follows:
- $\dfrac 1 {47} = 0 \cdotp \dot 02127 \, 65957 \, 44680 \, 85106 \, 38297 \, 87234 \, 04255 \, 31914 \, 89361 \, \dot 7$
This sequence is A021051 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Proof
Performing the calculation using long division:
0.021276595744680851063829787234042553191489361702... ------------------------------------------------------ 47)1.000000000000000000000000000000000000000000000000... 94 ---- 60 270 400 140 160 150 440 47 235 376 94 141 141 423 -- --- --- --- --- --- --- 130 350 240 460 190 90 170 94 329 235 423 188 47 141 --- --- --- --- --- -- --- 360 210 50 370 200 430 290 329 188 47 329 188 423 282 --- --- -- --- --- --- --- 310 220 300 410 120 70 80 282 188 282 376 94 47 47 --- --- --- --- --- -- -- 280 320 180 340 260 230 330 235 282 141 329 235 188 329 --- --- --- --- --- --- --- 450 380 390 110 250 420 100 423 376 376 94 235 376 94 --- --- --- --- --- --- --- 270 40 140 160 150 440 ...
$\blacksquare$