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Standard gravity is 9.80665 m/s2. That the number defined by the metric people who set all the world's units. In schools in the united states of america, we used 9.8. I don't recal using any more precision than that. Gravity at the surface does vary, but you don't need more presision than that for most academic purposes.
Is that so? I wonder what the story behind that is. Maybe it's a surface average?
Most people would probably guess this, but meters and seconds are defined independently of Earth's gravity, so it doesn't have a true value, just apparently a standard nominal one.
The value of g depends on altitude. You can define it easily at the earth average 0m altitude.
It also depends on latitude, and local geology and...
Maybe it is just weighted by surface area, you're right, and that's what I meant by "surface average".