Note that if we flip the sheet on which the digits are written, the digits $0,1,8$ will not change, 6 and 9 will swap places, and the others will lose their meaning. How many nine-digit numbers exist that do not change when the sheet is flipped?
All such numbers should consist of digits that make sense when the sheet is flipped, and the number is determined by its first five digits. Note that the fifth digit cannot be 6 or 9, and the first digit cannot be 0. Therefore, for the first digit, we have 4 options, for the second, third, and fourth digits - 5 each, and for the fifth digit - 3 options. Thus, the total number of such numbers is $4 \cdot 5^{3} \cdot 3=1500$.

## Answer

1500 numbers.