Q.Which of the following measurements is most precise?

The key idea is Least Count Precision: the smaller the least count (the smallest measurable division), the more precise the measurement. All options have the same numerical value (5.00) but different units.

Step 1: Identify the least count for each. A measurement like 5.00 implies precision to 0.01 of the given unit.

• (A) 5.00 mm → least count = 0.01 mm
• (B) 5.00 cm → least count = 0.01 cm = 0.1 mm
• (C) 5.00 m → least count = 0.01 m = 10 mm …

The key idea here is precision — not accuracy, not the size of the number, but how finely the measurement is made. A measurement is more precise if it can detect smaller changes. That’s captured by the least count: the smallest value that the instrument can reliably measure.

For a digital or scale reading, the least count is simply the place value of the last digit. All four options are written to two decimal places, but the unit changes the actual size of that last digit.

Let’s work through each option.

1. Option (A): 5.00 mm

   The last digit is in the hundredths place of a millimetre. So the least count is $0.01$ mm. That’s $1 \times 10^{-5}$ m.

2. Option (B): 5.00 cm

   Here the last digit is in the hundredths place of a centimetre. Least count = $0.01$ cm = $0.0001$ m = $1 \times 10^{-4}$ m.

3. Option (C): 5.00 m

   Last digit is hundredths of a metre. Least count = $0.01$ m = $1 \times 10^{-2}$ m.

4. Option (D): 5.00 km

   Last digit is hundredths of a kilometre. Least count = $0.01$ km = $10$ m = $1 \times 10^{1}$ m.

Method: Least Count (Precision) Analysis

Concept: The least count of a measurement is the smallest value it can measure reliably. A measurement is more precise when its least count is smaller — meaning it has more decimal places (or finer resolution) for the same unit.

Steps:

1. Convert all measurements to the same unit (here, metres).

   • (A) $5.00 \text{ mm} = 5.00 \times 10^{-3} \text{ m}$
   • (B) $5.00 \text{ cm} = 5.00 \times 10^{-2} \text{ m}$
   • (C) $5.00 \text{ m}$ (already in metres)
   • (D) $5.00 \text{ km} = 5.00 \times 10^{3} \text{ m}$

2. Identify the least count for each — the smallest place value in the given unit.

   • All four have two decimal places in their original unit.
   • But precision depends on the absolute size of the least count in metres.

3. Compute the least count in metres:

   • (A) $0.01 \text{ mm} = 0.01 \times 10^{-3} \text{ m} = 1 \times 10^{-5} \text{ m}$
   • (B) $0.01 \text{ cm} = 0.01 \times 10^{-2} \text{ m} = 1 \times 10^{-4} \text{ m}$ …

Common Mistakes & How to Avoid Them

Mistake 1: Confusing "Precision" with "Accuracy"

The error: Students think a larger unit (like km) is "more precise" because it's a bigger number, or that all measurements with the same number of decimal places are equally precise.

Why it's wrong: Precision is about the smallest measurable change — the least count — not the size of the quantity.

• 5.00 mm has a least count of 0.01 mm (10 µm)
• 5.00 km has a least count of 0.01 km = 10 m

So 5.00 mm is far more precise because it can detect much smaller differences.

How to avoid: Always convert every measurement to the same unit (preferably the smallest unit present) and then compare the least count (the place value of the last digit).

Mistake 2: Ignoring the Unit When Comparing Decimal Places

The error: Seeing "5.00" in all options and assuming they are equally precise.

Why it's wrong: The decimal places are in different units.

• 5.00 cm means precision to 0.01 cm = 0.1 mm
• 5.00 mm means precision to 0.01 mm = 0.01 mm

The unit determines what that last digit actually represents.

How to avoid: Write the least count explicitly for each option:

Now compare — smallest least count = most precise.

Mistake 3: Thinking "More Significant Figures = More Precise"

The error: Counting the number of significant figures without considering the unit.

Why it's wrong: All four options have 3 significant figures. But the actual precision depends on what those figures represent in real-world length. …