The text is mistranscribed. The original says...
Q: Is there anything that contains hydrogen that is not a fuel?
A: Yes, there is water, the weight of which is one - eighth hydrogen
Crucially, there's no of before hydrogen.
Asimov isn't saying that water weighs only an eighth as much as hydrogen - he's saying that one eighth of the weight of water comes from the hydrogen it contains - along with oxygen, one atom of which which is 16 times heavier than a hydrogen atom (but water is H2O, and 16/2=8).
EDIT: It's fully covered in comments, but in fact Asimov should have said that for any given weight of water, 1/9th comes from the hydrogen it contains (16 from one atom of oxygen plus 2 atoms of hydrogen gives 18, so hydrogen's contribution to "total weight" = 2/18 = 1/9). But this doesn't affect the syntax.