Earth’s current distance from its location 100 years ago has to be relative to a chosen reference point as everything in the universe is moving in relation to everything else, so there is no absolute position like you have on your GPS on Earth’s finite surface.
If you want to total up all of Earth’s known movements you could get distance traveled which does not reference a specific location:
Earth orbits the Sun once a year, distance 940 million km x 100 = 94 billion km or ~ 9.4 x 10^10 km
The Solar System is in orbit around the center of the Milky Way galaxy, traveling 230 km/s in reference to the galactic center for 100 years = ~ 7.253 x 10^11 km
If you want to get a speed of the Milky Way a reference point could be the Cosmic Microwave Background rest state which gives our galaxy ~ 631 km/s, giving the Milkway way a 100 year distance of: 1.98992 x 10^12 km
So if you sum these 3 distances:
9.4 x 10^10
72.53 x 10^10
198.992 x 10^ 10
for a total of:
280.922 x 10^10 km = ~ 2.81 trillion km which is about 30% of a light year (0.3 LY)
How far that 0.3 light years is from the position of the Earth 100 years ago depends on what you use for a point of reference.
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