JEE PYQ: Units & Measurements - Question ID 0ad65b309b4c (JEE Main 2026)

Core Formula & Concept:

In the chapter Units & Measurements, one of the key concepts is significant figures (sig-figs). Significant figures indicate the precision of a measured or calculated quantity. When adding or subtracting physical quantities, the result must be reported with the same number of decimal places as the quantity with the fewest decimal places.

The rule is:

• Identify the number with the least precision (i.e., fewest decimal places).
• Round the final sum to match that precision.

This ensures that the result does not imply a false level of precision beyond what the measurements allow.

Step-by-Step Derivation:

We are given three physical quantities to add:

• $52.01 \text{ m}$ (4 sig-figs, 2 decimal places)
• $153.2 \text{ m}$ (4 sig-figs, 1 decimal place)
• $0.123 \text{ m}$ (3 sig-figs, 3 decimal places)

Step 1: Perform the arithmetic addition

Add the three values directly: $52.01 + 153.2 + 0.123 = 205.333 \text{ m}$

Step 2: Identify the least precise measurement

Among the three:

• $52.01$ has 2 decimal places.
• $153.2$ has 1 decimal place.
• $0.123$ has 3 decimal places.

The least precise is $153.2 \text{ m}$, with only 1 decimal place.

Step 3: Round the sum to match the least precision

The raw sum is $205.333 \text{ m}$. Since we must round to 1 decimal place:

• Look at the second decimal digit: 3 (in 205.333).
• Since 3 < 5, we do not round up the first decimal digit.

Thus, $205.333 \text{ m}$ rounded to 1 decimal place is $205.3 \text{ m}$.

Step 4: Match with the given options

The correctly rounded sum is $205.3 \text{ m}$, which corresponds to Option A.

Common Traps & Exam Tip:

Students often make the following mistakes:

• Ignoring decimal places: They might add all digits and report $205.333 \text{ m}$ (Option C), forgetting to round based on the least precise measurement.
• Rounding to significant figures instead of decimal places: They may count total sig-figs (e.g., 3 sig-figs) and incorrectly round to $205 \text{ m}$ (Option B).
• Over-rounding: They might see $153.2$ and think it has no decimal precision, leading to $205 \text{ m}$ (Option B).

Exam Tip: Always focus on decimal places, not total significant figures, when adding or subtracting. The rule is about precision in the fractional part, not the total number of meaningful digits.