Round the value 2.55 off to 2 significant digits.

The given number is $2.55$.

To round it off to $2$ significant digits, the digit to be dropped is $5$.

According to the rules of rounding off, if the digit to be dropped is $5$ and it is not followed by any non-zero digits, the preceding digit is increased by $1$ if it is odd, and left unchanged if it is even.

In $2.55$, the preceding digit is $5$, which is an odd number.

Therefore, the preceding digit is increased by $1$.

Thus, $2.55$ rounded off to $2$ significant digits is $2.6$.