This is fun! but not so surprising to me:

987,654,321 + 123,456,789 = 1,111,111,110

1,111,111,110 + 123,456,789 = 1,234,567,899 \approx 1,234,567,890

So 987,654,321 + 2 x 123,456,789 \approx 10 x 123,456,789

Thus 987,654,321 / 123,456,789 \approx 8.

If you squint you can see how it would work similarly in other bases. Add the 123... equivalent once to get the base-independent series of 1's, add a second time to get the base-independent 123...0.