Convert it to hexidecimal? If the system stores things as binary, it's going to store it as binary no matter how you wish to display it. It's not as if one hex digit fits in one binary digit therefor you can just convert everything to hex and save space. I don't think they're looking to just store a string directly, I think they want to maintain the same exact bytes. I'm honestly not sure what floating point looks like in hex, but I have a feeling it's representation would be only slightly shorter than just the decimal representation of the string.
EDIT: For strings -- here is double precision in decimal vs hex
Code:
3.1415926535897930
400921FB54442D18
So two bytes. I suppose it shrinks it a bit, but I don't think it's small enough for what the OP wants.
EDIT 2: ...and lastly, which I probably should have thought of first, isn't converting to hex on one comp and back on another subject to the same rounding errors as just sending the double directly would have?