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

Options

A. `2.75 and 2.74`
B. `2.74 and 2.73`
C. `2.75 and 2.73`
D. `2.74 and 2.74`

Explanation

To round off the numbers 2.745 and 2.735 to three significant figures, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Significant Figures**:
- For both numbers, we need to consider the first three digits from the left.
- For 2.745, the significant figures are 2, 7, and 4.
- For 2.735, the significant figures are 2, 7, and 3.

2. **Look at the Fourth Digit**:
- For rounding, we need to look at the digit immediately after the third significant figure (the fourth digit).
- In 2.745, the fourth digit is 5.
- In 2.735, the fourth digit is also 5.

3. **Apply the Rounding Rule**:
- The rounding rule states that if the digit after the last significant figure (the fourth digit) is 5, we look at the third digit (the last significant figure).
- If the third digit is even, we do not change it. If it is odd, we increase it by 1.

4. **Evaluate 2.745**:
- The third digit is 4 (even), and the fourth digit is 5.
- Since 4 is even, we keep the third digit the same.
- Therefore, 2.745 rounded to three significant figures is **2.74**.

5. **Evaluate 2.735**:
- The third digit is 3 (odd), and the fourth digit is 5.
- Since 3 is odd, we increase the third digit by 1.
- Therefore, 2.735 rounded to three significant figures is also **2.74**.

### Final Answers:
- Both 2.745 and 2.735 rounded to three significant figures give **2.74**.