Actually, there is an integer multiple... or rather, an integer ratio. Since we are talking about land, we have to use US Survey measurements. A Survey Foot is, by definition, 1200/3937 metres. So an acre, being 43560 square feet, would be 43560*(1200/3937)^2 or 62726400000/15499969 square metres. There are 10000 square metres in a hectare, so an acre is 6272640/15499969 hectares exactly*.
*At least, in some states. Not all states use survey feet. Some use customary feet, which changes the numbers slightly. However, since both customary feet and survey feet are, by definition, exact fractions of the metre, the argument still holds. Only the numbers would change. Of course, the underlying data (The US National Spatial Reference System NAD 83(2011/MA11/PA11) epoch 2010.00) is metric from the outset and is converted to feet for publication.