Because there could still be too much of the solid part for it to have a density less than air's?
edit: i suspect it would float for a little bit before the lighter gas diffuses out
Wikipedia says
The lowest-density aerogel is a silica nanofoam at 1 mg/cm3,[6] which is the evacuated version of the record-aerogel of 1.9 mg/cm3.[7] The density of air is 1.2 mg/cm3 (at 20 °C and 1 atm).[8] Only the recently manufactured metallic microlattices have a lower density at 0.9 mg/cm3.[9] By convention, the mass of air is excluded when the microlattice density is calculated. Allowing for the mass of the interstitial air, the true, unevacuated density of the microlattice is approximately 2.1 mg/cm3 (2.1 kg/m3).
So the evacuated version with 1mg...
I have a whimsical challenge for you: come up with problems with numerical solutions that are hard to estimate.
This, like surprisingly many things, originates from a Richard Feynman story:
So what would you ask Richard Feynman to solve? Think of this as the reverse of Fermi Problems.
Number theory may be a rich source of possibilities here; many functions there are wildly fluctuating, require prime factorization and depend upon the exact value of the number rather than it's order of magnitude. For example, I challenge you to compute the largest prime factor of 650238.
(My original example was: "For example, I challenge you to compute the greatest common denominator of 10643 and 15047 without a computer. This problem has the nice advantage of being trivial to make harder to compute - just throw in some extra primes." It has been pointed out that I forgot Euclid's algorithm and have managed to choose about the only number theoretic question that does have an efficient solution.)