Final answer:
Barack Obama won all of Ohio's electoral votes by securing 51 percent of the popular vote, reflecting the winner-take-all system used by most states.
Step-by-step explanation:
When Barack Obama won 51 percent of the popular vote in Ohio, he won all of the state’s electoral votes. This is because Ohio, like the majority of states, uses a winner-take-all system for allocating electoral votes. According to this system, regardless of whether a candidate wins by a slim margin or a landslide, as long as they have the majority of the popular vote, they receive all of the electoral votes from that state. This system is in contrast with states like Maine and Nebraska, which use a congressional district method, where electoral votes can be split based on congressional district outcomes.