Number of seconds in a year
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The Labrigger editorial team was a little disappointed in the consistently excellent xkcd when the recently posted list of approximations included:
Number of seconds in a year = 75^4 (accurate to 1 part in 400)
and
Number of seconds in a year = 525600 x 60 (accurate to 1 part in 1400)
In our physics classes, we always used:
Number of seconds in a year = Pi x 10^7 (accurate to 1 part in 200)
It’s still very accurate. And most importantly, the factor of Pi makes for some fascinating cancellations in calculations.