Mathematical coincidences

Unexpected approximate relations between trascendental numbers can be intriguing. You can read in Wikipedia about many of them. One can have fun looking for new coincidences. So far I found the following:

π≈ π to , with 0.0006% error.

π≈ π to , with 0.0002% error.

e ≈ e , with 0.000 000 03% error.

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