Reciprocal of 53
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Theorem
The decimal expansion of the reciprocal of $53$ is as follows:
- $\dfrac 1 {53} = 0 \cdotp \dot 01886 \, 79245 \, 28 \dot 3$
This sequence is A021057 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Proof
Performing the calculation using long division:
0.018867924528301... --------------------- 53)1.000000000000000000 53 212 -- --- 470 280 424 265 --- --- 460 150 424 106 --- --- 360 440 318 424 --- --- 420 160 371 159 --- --- 490 100 477 53 --- --- 130 ... 106 --- 240 212 ---
$\blacksquare$