A) In multiplication or division, the final result should retain only that many significant figures as are there in the original number with the least number of significant figures.
B) In addition or subtraction the final result should retain only that many decimal places as are there in the number with the least number of decimal places.

Options

A. Only A is correct
B. A, B are correct
C. Only B is correct
D. A, B are wrong

Answer

To solve the question regarding the rules of significant figures in multiplication/division and decimal places in addition/subtraction, we will analyze both statements step by step.

### Step 1: Understand the Rule for Multiplication/Division
The first statement asserts that in multiplication or division, the final result should retain only that many significant figures as are in the original number with the least number of significant figures.

**Example:**
- Consider the numbers 1.23 (3 significant figures) and 2.345 (4 significant figures).
- When we multiply these numbers:
\[ 1.23 \times 2.345 = 2.88435 \]
- The number with the least significant figures is 1.23 (which has 3 significant figures).
- Therefore, we round 2.88435 to 3 significant figures:
\[ \text{Final result} = 2.88 \]

### Step 2: Understand the Rule for Addition/Subtraction
The second statement states that in addition or subtraction, the final result should retain only that many decimal places as are in the number with the least number of decimal places.

**Example:**
- Consider the numbers 1.23 (2 decimal places) and 2.345 (3 decimal places).
- When we add these numbers:
\[ 1.23 + 2.345 = 3.575 \]
- The number with the least decimal places is 1.23 (which has 2 decimal places).
- Therefore, we round 3.575 to 2 decimal places:
\[ \text{Final result} = 3.58 \]

### Step 3: Conclusion
Both statements are correct based on the rules of significant figures and decimal places in calculations.

### Final Answer
Both A and B are correct.

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