Reciprocal of 21
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Theorem
The decimal expansion of the reciprocal of $21$ is as follows:
- $\dfrac 1 {21} = 0 \cdotp \dot 04761 \, \dot 9$
This sequence is A021025 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Proof
Performing the calculation using long division:
0.04761901... -------------- 21)1.00000000000 84 -- 160 147 --- 130 126 --- 40 21 --- 190 189 --- 100 84 --- ...
$\blacksquare$
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $47,619$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $47,619$