1988 AHSME Problem 10

In an experiment, a scientific constant C is determined to be 2.43865 with an error of at most \pm 0.00312. The experimenter wishes to announce a value for C in which every digit is significant. That is, whatever C is, the announced value must be the correct result when C is rounded to that number of digits. The most accurate value the experimenter can announce for C is

\textbf{(A)}\ 2\qquad \textbf{(B)}\ 2.4\qquad \textbf{(C)}\ 2.43\qquad \textbf{(D)}\ 2.44\qquad \textbf{(E)}\ 2.439

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.