Reciprocal of 43
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Theorem
The decimal expansion of the reciprocal of $43$ is as follows:
- $\dfrac 1 {43} = 0 \cdotp \dot 02325 \, 58139 \, 53488 \, 37209 \, \dot 3$
This sequence is A021047 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Proof
Performing the calculation using long division:
0.02325581395348837209302... ----------------------------- 43)1.00000000000000000000000... 86 ---- 140 410 310 129 387 301 --- --- --- 110 230 90 86 215 86 --- --- -- 240 150 400 215 129 387 --- --- --- 250 210 130 215 172 129 --- --- --- 350 380 100 344 344 86 --- --- --- 60 360 ... 43 344 -- --- 170 160 129 129 --- --- 410 310
$\blacksquare$