Heh, I reasoned about the exponent by hand and got -55 but then wasn't sure whether it was correct so I searched for discussions of 0.3 - 0.2 - 0.1 and took the

Heh, I reasoned about the exponent by hand and got -55 but then wasn't sure whether it was correct so I searched for discussions of 0.3 - 0.2 - 0.1 and took the value they quoted (2^-54). That being an off-by-one error does resolve my question.