Borrowing from the tradition of the ancient Greeks, the first ones
who tried to describe the brightness of stars with numbers ...
6 magnitudes = a ratio of 100 .
In more modern notation . . .
1 magnitude = ratio of (100) ^ (1/6)
= about 2.154...
9.6 magnitudes = (100) ^ (9.6/6)
= 100¹·⁶
= 1,584.89 (rounded)