Question

Keeping the significant figures in view, the sum of the physical quantities $52.01$ m, $153.2$ m and $0.123$ m is :

• A. $205.33$ m
• B. $205.333$ m
• C. $205$ m
• D. $205.3$ m

Hint:

For addition/subtraction: look at decimal places. For multiplication/division: look at the total number of significant figures.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
When adding or subtracting physical quantities, the result should be reported to the same number of decimal places as the measurement with the fewest decimal places.

Step 2: Detailed Explanation:
The quantities given are:
1. $52.01$ m (2 decimal places)
2. $153.2$ m (1 decimal place)
3. $0.123$ m (3 decimal places)
Performing the mathematical sum:
\[ 52.01 + 153.2 + 0.123 = 205.333 \text{ m} \]
Since the least precise measurement ($153.2$ m) has only one decimal place, the final answer must be rounded to one decimal place.
Rounding $205.333$ to one decimal place gives $205.3$.

Step 3: Final Answer:
The sum with significant figures is $205.3$ m.