The numbers 2.745 and 2.735 on rounding off to 3 significant figures will give

The correct option is "2.74 and 2.74".

To understand why both numbers round to 2.74 when rounded to 3 significant figures, we must apply the rules of rounding off, specifically the rule concerning the digit 5.

The general rules for rounding off a number to a desired number of significant figures are as follows:
1. If the digit next to the last significant digit is greater than 5, the last significant digit is increased by 1.
2. If the digit next to the last significant digit is less than 5, the last significant digit is left unchanged.
3. If the digit next to the last significant digit is exactly 5 (or 5 followed by only zeros), then we look at the preceding digit (the last significant digit):
    • If the preceding digit is even, it is left unchanged.
    • If the preceding digit is odd, it is increased by 1 (to make it even).

Let's apply these rules to each of the given numbers:

1. Rounding 2.745 to 3 significant figures:
The first three significant figures are 2, 7, and 4. The digit following the third significant figure is 5.
Since the digit to be dropped is exactly 5, we look at the preceding digit, which is 4.
Because 4 is an even number, it is left unchanged.
Therefore, 2.745 rounds to 2.74.

2. Rounding 2.735 to 3 significant figures:
The first three significant figures are 2, 7, and 3. The digit following the third significant figure is 5.
Since the digit to be dropped is exactly 5, we look at the preceding digit, which is 3.
Because 3 is an odd number, it is increased by 1 to make it even (3 + 1 = 4).
Therefore, 2.735 rounds to 2.74.

Hence, rounding both 2.745 and 2.735 to 3 significant figures gives 2.74 and 2.74, respectively.