To express the number 2.1777 using bar notation, we need to identify the repeating part of the decimal. In this case, if the "77" is the part that repeats, it can be denoted as:
\[ 2.1\overline{77} \]
This means that the "77" repeats indefinitely after the "1". If the entire decimal were to repeat, we would express it differently, but based on the given number, the notation above is the appropriate representation.