From Wikipedia, the definition of the meter is
The meter is defined as the distance traveled by light in a vacuum in 1/299792458 seconds.
Why is this number of seconds chosen? Is there a motivation for this choice?
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1 Answer
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Yes and no.
Yes - because one can pick any distance one wants, and call it a meter (originally, it was 1/40,000,000th of the circumference of Earth measured over the poles; then the distance between a pair of lines on a standard platinum rod, then...).
But no - it is specifically chosen to be that value because
a) we believe the speed of light to be an absolute constant in the universe
b) by defining distance in terms of speed of light (a constant) and time (something we can measure precisely) we no longer need to maintain two separate standards.
The number was chosen such that the speed of light (which was previously known to be approximately 299,792,458 m/s) will henceforth be exactly that number.
Much detail on this can be found in this question and the associated answers. Note that that question asks the converse of this one - namely, "why does the speed of light have no uncertainty". This is the other half of that question.
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