I have to admit, though: I didn't want to go throught the same level of work as Scott did (great explanation, by the way); nor did I want to "cheat" by copy-paste-execute, so I guessed (correctly, as it turned out).
I cheated because I knew about the incomplete correspondence between decimals and binaries, and did not want to guess. But now I have found a great website for decimal-to-IEEE754 conversion: http://www.binaryconvert.com
This site shows hexadecimal and binary representation of an entered number, as well as the most accurate result of the conversion from this binary back to decimal.
Here is the result for 165.755 (double precision):
01000000 01100100 10111000 00101000
11110101 11000010 10001111 01011100
The result of backward conversion to decimal: 1.65754999999999995452526491135E2
The same for 165.555:
01000000 01100100 10110001 11000010
10001111 01011100 00101000 11110110
With these values the correct answer becomes obvious