JEE PYQ: Units & Measurements - Question ID 9c724138783c (JEE Main 2025)

Core Formula & Concept:

In the chapter Units & Measurements, one of the key concepts is the rule for arithmetic operations with significant figures. When adding or subtracting measured quantities, the result must be reported with the same number of decimal places as the measurement with the fewest decimal places. This ensures that the precision of the result is not overstated.

Given three masses:

• $m_1 = 435.42 \text{ g}$ (2 decimal places)
• $m_2 = 226.3 \text{ g}$ (1 decimal place)
• $m_3 = 0.125 \text{ g}$ (3 decimal places)

The sum must be rounded to the least number of decimal places among the three, which is 1 decimal place (from $m_2$).

Step-by-Step Derivation:

Step 1: Align the numbers by decimal place
Write all masses with the same number of decimal places for clarity:

• $435.420 \text{ g}$
• $226.300 \text{ g}$
• $0.125 \text{ g}$

Step 2: Perform the addition
Add the masses directly: $435.420 + 226.300 + 0.125 = 661.845 \text{ g}$

Step 3: Apply the significant figures rule for addition
The measurement with the fewest decimal places is $226.3 \text{ g}$ (1 decimal place). Thus, the result must be rounded to 1 decimal place.
Rounding $661.845$ to 1 decimal place:

• The digit in the first decimal place is 8.
• The digit in the second decimal place is 4, which is less than 5, so we do not round up the first decimal digit.

Thus, the rounded result is $661.8 \text{ g}$.

Step 4: Match with the given options
The correct answer is Option D: $661.8 \text{ g}$.

Common Traps & Exam Tip:

Trap 1: Ignoring the rule for addition/subtraction
Students often apply the multiplication/division rule (counting significant figures) instead of the addition/subtraction rule (counting decimal places). This leads to incorrect rounding.

Trap 2: Overlooking the least precise measurement
Some students mistakenly round based on the measurement with the most decimal places (e.g., $0.125 \text{ g}$) instead of the fewest ($226.3 \text{ g}$).

Exam Tip:
Always align the numbers by decimal place before adding or subtracting. This makes it easier to identify the measurement with the fewest decimal places and apply the rounding rule correctly.