Assertion: A number 2.746 rounded off to three significant figures is 2.75, while the number 2.743 would be 2.74.
Reason: In rounding off the uncertain digits, the preceding digit is raised by 1 if the insignificant digit to be dropped is more than 5 and is left unchanged if the latter is less than 5.

Options

A. if both assertion and reason are true reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation fo assertion.
C. If assertion is true but reaso is false.
D. IF both assertion and reason are false.

Explanation

To solve the question, we need to analyze the assertion and the reason provided, and determine their correctness.

### Step 1: Analyze the Assertion
The assertion states that:
- The number 2.746 rounded off to three significant figures is 2.75.
- The number 2.743 rounded off to three significant figures is 2.74.

**Rounding off 2.746:**
- The third significant figure is 6 (in the hundredths place).
- The digit following it (the fourth significant figure) is 6.
- Since 6 is greater than 5, we round up the third significant figure (6) to 7.
- Therefore, 2.746 rounded to three significant figures is indeed **2.75**.

**Rounding off 2.743:**
- The third significant figure is 4 (in the hundredths place).
- The digit following it (the fourth significant figure) is 3.
- Since 3 is less than 5, we do not change the third significant figure (4).
- Therefore, 2.743 rounded to three significant figures is **2.74**.

**Conclusion for Assertion:**
The assertion is **true**.

### Step 2: Analyze the Reason
The reason states:
- In rounding off, the preceding digit is raised by 1 if the insignificant digit to be dropped is more than 5, and is left unchanged if it is less than 5.

This statement correctly describes the rounding rules:
- If the digit to be dropped is greater than 5, you round up.
- If the digit to be dropped is less than 5, you do not change the preceding digit.

**Conclusion for Reason:**
The reason is also **true** and correctly explains the assertion.

### Final Conclusion
Both the assertion and the reason are true, and the reason is a correct explanation of the assertion.

### Answer:
Both assertion and reason are true, and the reason is a correct explanation of the assertion.

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