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

To find the sum of the given physical quantities while considering significant figures, we must pay attention to the number of decimal places in each quantity. The rule for addition and subtraction is that the result should have the same number of decimal places as the quantity with the least number of decimal places.

1. Review the given quantities:
   • $52.01$ m has two decimal places.
   • $153.2$ m has one decimal place.
   • $0.123$ m has three decimal places.
2. Identify the quantity with the least number of decimal places, which is $153.2$ m with one decimal place.
3. Add the quantities:
   • $52.01 \, \text{m} + 153.2 \, \text{m} + 0.123 \, \text{m} = 205.333 \, \text{m}$
4. Round the result to have the same number of decimal places as the quantity with the least number of decimal places:
   • Since $153.2$ m has one decimal place, the sum should be rounded to one decimal place.
   • Therefore, $\text{round}(205.333 \, \text{m}) = 205.3 \, \text{m}$.

Thus, the correct sum of the physical quantities, considering significant figures, is 205.3 \, \text{m}.

Therefore, the correct answer is $205.3$ m.