Your teacher has decided that one person in your class will get an extra $50$ points of credit. The lucky person has been narrowed down, so now it is between you and Newton. The teacher says, “I'm thinking of a number between $\mathit{0}$ and $\mathit{10}$. Whoever can choose the number closest to it gets the $\mathit{50}$ points.” Quickly, Newton yells out, “Three!” What number would you choose? Justify and explain your answer.