JEE PYQ: Units & Measurements - Question ID 70141955849d (JEE Main 2024)

In the chapter Units & Measurements, one of the key concepts is Significant Figures. Significant figures (or significant digits) are the digits in a number that carry meaning contributing to its precision. This includes all digits except:

• Leading zeros (zeros before the first non-zero digit), which are only placeholders.
• Trailing zeros in a number without a decimal point, which may or may not be significant depending on context (but in scientific notation or with a decimal, they are significant).

The rules for determining significant figures are:

1. All non-zero digits are significant.
2. Zeros between non-zero digits are significant.
3. Leading zeros are not significant.
4. Trailing zeros in a number containing a decimal point are significant.
5. Trailing zeros in a whole number without a decimal point are not significant (unless specified otherwise, e.g., via scientific notation).

Using these rules, we count the significant figures in each number in List I and match them with the corresponding entries in List II.

Step 1: Analyze (A) 1001

Number: $1001$
- All digits are non-zero or zeros between non-zero digits.
- The zeros are between 1s, so they are significant.
- Total significant figures: $4$
⇒ Matches with (II)

Step 2: Analyze (B) 010.1

Number: $010.1$
- Leading zero (before the first non-zero digit) is not significant.
- The digits $1$, $0$, and $1$ are significant.
- The zero between two non-zero digits is significant.
- So, significant digits: $1$, $0$, $1$ → 3 significant figures.
⇒ Matches with (I)

Step 3: Analyze (C) 100.100

Number: $100.100$
- All non-zero digits: $1$, $0$, $0$, $1$ are significant.
- Trailing zeros after the decimal point are significant.
- So, digits: $1$, $0$, $0$, $1$, $0$, $0$ → all 6 are significant.
⇒ Matches with (IV)

Step 4: Analyze (D) 0.0010010

Number: $0.0010010$
- Leading zeros (before the first non-zero digit) are not significant.
- First non-zero digit is $1$, then $0$, $0$, $1$, and the final $0$ after the decimal is significant.
- Significant digits: $1$, $0$, $0$, $1$, $0$ → 5 significant figures.
⇒ Matches with (III)

Step 5: Match with Options

From above:
- (A) → (II)
- (B) → (I)
- (C) → (IV)
- (D) → (III)

This corresponds to Option A.

Students often make the following mistakes:

1. Counting leading zeros: Many students mistakenly count leading zeros (e.g., in 010.1 or 0.0010010) as significant. Remember: leading zeros are never significant.
2. Ignoring trailing zeros after decimal: In numbers like 100.100, students may overlook the trailing zeros after the decimal, thinking they are not significant. But they are significant because they indicate precision.
3. Confusing whole number trailing zeros: In numbers like 1000 (without decimal), trailing zeros are not significant unless specified. But in 100.100, the trailing zeros are significant due to the decimal point.
4. Misreading the number format: Students sometimes misread 010.1 as having 4 digits, but the leading zero is not counted.

Exam Tip: Always underline or circle the first non-zero digit and count from there. Zeros after that are significant if they are between non-zero digits or after a decimal point.

Also, double-check whether the number has a decimal point — it changes everything for trailing zeros!