In the rules it states "The Player pays at least half (rounded down) of a building's tile cost..." but if you round down, you won't be paying at least half. Shouldn't it be round up so that if a building costs 9 (half 4.5), you pay 5 (rounded up) instead of 4 (rounded down). This makes it so you are paying at least half...
You always have to make concessions for odd amounts when halving an amount. In this case, they have opted to round down instead of round up.
The "at least half" refers to the fact that you can overpay and (typically) don't get change back. So it is not that you have to pay 50% or more to take the tile, You have to pay half (rounded down) but given how the game works, you can still overpay.
I think it is fine and a moot point since you have to pay the full amount for the tile eventually. that one money difference really isn't that big of a deal in the long run, again, especially because over-payment is already present in the game.