NASA is preparing to launch a rocket into space. It is determined that the angle $($in degrees$)$ that the rocket needs to point is equivalent to the following alternating series: ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{(-1{)}^{n+1}*120}{(n+1)!}$ NASA needs the angle to be accurate to $10$ decimal places. What is the minimum number of terms they need to get the desired accuracy?

$10$ terms

$15$ terms

$16$ terms

$13$ terms

$14$ terms