Also, adding 123456789 to itself eight times on an abacus is a nice exercise, and it's easy to visually control the end result.
base 16: 123456789ABCDEF~16 * (16-2) + 16 - 1 = FEDCBA987654321~16
base 10: 123456789~10 * (10-2) + 10 - 1 = 987654321~10
base 9: 12345678~9 * (9-2) + 9 - 1 = 87654321~9
base 8: 1234567~8 * (8-2) + 8 - 1 = 7654321~8
base 7: 123456~7 * (7-2) + 7 - 1 = 654321~7
base 6: 12345~6 * (6-2) + 6 - 1 = 54321~6
and so on..
or more generally:
base n: sequence * (n - 2) + n - 1
num(b)/denom(b) = b - 2 + (b-1)/denom(b)
They are also +9 away from being in order.
And then 12345678 * 8 is 98765424 which is +9 away from also being in order.
For binary, it looks like (1-(b-1))/1=b-10 or (1-(2-1))/1=2-2=0 in decimal.
For trinary, it looks like (21-(b-1))/12=b-2 or (7-(3-1))/5=5/5=1 in decimal.
For quaternary, it looks like (321-(b-1))/123=b-2 or (57-(4-1))/27=54/27=2 in decimal.
Essentially and perhaps unsurprisingly, the size of the slices in the number pie get smaller the bigger the pie gets. In binary, the slice is the pie, which is why the division comes out to zero there.
12345679 * 8 = 98765432