MCQEasyJEE 2026Significant Figures & Error Analysis

JEE Physics 2026 Question with Solution

Keeping the significant figures in view, the sum of the physical quantities 52.01m52.01 \, \text{m}, 153.2m153.2 \, \text{m} and 0.123m0.123 \, \text{m} is :

  • A

    205.33m205.33 \, \text{m}

  • B

    205.333m205.333 \, \text{m}

  • C

    205m205 \, \text{m}

  • D

    205.3m205.3 \, \text{m}

Answer

Correct answer:D

Step-by-step solution

Standard Method

Given: The quantities are 52.01m52.01 \, \text{m}, 153.2m153.2 \, \text{m} and 0.123m0.123 \, \text{m}.

Find: The correct sum keeping significant figures in view.

When physical quantities are added, the result must be reported to the same number of decimal places as the quantity with the fewest decimal places.

Here:

  • 52.01m52.01 \, \text{m} has 22 decimal places
  • 153.2m153.2 \, \text{m} has 11 decimal place
  • 0.123m0.123 \, \text{m} has 33 decimal places

So the final answer must be rounded to one decimal place.

First, add the given quantities:

52.01+153.2+0.123=205.333m52.01 + 153.2 + 0.123 = 205.333 \, \text{m}

Now round 205.333m205.333 \, \text{m} to one decimal place:

205.333m205.3m205.333 \, \text{m} \approx 205.3 \, \text{m}

Therefore, the sum with significant figures is 205.3m205.3 \, \text{m}. The correct option is D.

Common mistakes

  • Using the rule for multiplication or division here is incorrect. For addition, the limiting factor is the number of decimal places, not the total number of significant figures. Always round the final sum based on the least number of decimal places.

  • Choosing 205.333m205.333 \, \text{m} without rounding is incorrect because it keeps more decimal places than justified by the least precise measurement. After adding, round the result to one decimal place.

  • Rounding each term before adding can change the result unnecessarily. First add all the given values as written, then round only the final answer according to the decimal-place rule.

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