JEE PYQ: Units & Measurements - Question ID f291d8c8abdf (JEE Main 2019)

In the chapter Units & Measurements, one of the key concepts is significant figures (sig-figs). Significant figures represent the precision of a measured or calculated quantity. When performing arithmetic operations (like multiplication or addition), the result must be reported with the correct number of significant figures to reflect the precision of the least precise input.

For multiplication or division, the rule is:

• The result should have the same number of significant figures as the input with the fewest significant figures.

In this problem:

• The area of one square is given as $5.29 \text{ cm}^2$. This has 3 significant figures.
• We are multiplying this area by 7 (an exact integer, which has infinite significant figures).

Step 1: Identify the given data and significant figures
Area of one square = $5.29 \text{ cm}^2$ (3 significant figures).
Number of squares = 7 (exact integer, infinite significant figures).

Step 2: Perform the multiplication
Total area = Area of one square × Number of squares
$= 5.29 \text{ cm}^2 \times 7$
$= 37.03 \text{ cm}^2$.

Step 3: Apply significant figures rule
Since $5.29$ has 3 significant figures, the result must also be reported with 3 significant figures.
$37.03 \text{ cm}^2$ rounded to 3 significant figures is $37.0 \text{ cm}^2$.

Step 4: Match with the given options
The correct answer is A: $37.0 \text{ cm}^2$.

Trap 1: Ignoring significant figures
Many students compute $5.29 \times 7 = 37.03$ and directly select option D ($37.03 \text{ cm}^2$), forgetting to round to the correct number of significant figures. This is incorrect because the precision of the result must match the least precise input (3 sig-figs here).

Trap 2: Misinterpreting the decimal
Some students might think $37.0$ has only 2 significant figures (due to the trailing zero after the decimal). However, the zero after the decimal is significant because it indicates precision. Thus, $37.0$ has 3 significant figures.

Exam Tip:
Always check the significant figures of all given quantities before performing arithmetic operations. For multiplication/division, the result must have the same number of sig-figs as the input with the fewest sig-figs. Exact integers (like 7 in this case) do not affect the sig-fig count.