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 solve the problem of rounding the numbers 2.745 and 2.735 to three significant figures, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Significant Figures**:
- The number 2.745 has four significant figures (2, 7, 4, and 5).
- The number 2.735 also has four significant figures (2, 7, 3, and 5).

2. **Rounding the First Number (2.745)**:
- To round 2.745 to three significant figures, we look at the fourth significant figure, which is 5.
- According to the rounding rules, if the last digit (5 in this case) is followed by an even digit, we do not change the preceding digit. Since the digit before 5 (which is 4) is even, we keep it as is.
- Therefore, 2.745 rounded to three significant figures is **2.74**.

3. **Rounding the Second Number (2.735)**:
- Now, we round 2.735 to three significant figures. Again, we look at the fourth significant figure, which is 5.
- However, the digit before 5 (which is 3) is odd. According to the rounding rules, if the preceding digit is odd, we increase it by 1 to make it even.
- Thus, we increase 3 by 1, resulting in 4.
- Therefore, 2.735 rounded to three significant figures is also **2.74**.

4. **Final Result**:
- The rounded values for both numbers are:
- 2.745 → 2.74
- 2.735 → 2.74

### Conclusion:
The final rounded values for both numbers are **2.74** and **2.74**.