What is the least possible error encountered when taking measurement with a metre rule?

Analysis

The question asks for the "least possible error" (also known as the uncertainty or precision) when using a standard metre rule. In physics, the uncertainty of a measuring instrument is generally taken as half of its smallest scale division.

Concept: Precision of Measuring Instruments

A standard metre rule is calibrated in centimetres (cm) and millimetres (mm).

• The smallest marking on a metre rule is 1 mm (or 0.1 cm).
• When you take a measurement, you can typically estimate to the nearest half of the smallest division (e.g., if the object falls between 12 mm and 13 mm, you might estimate it as 12.5 mm).
• Therefore, the uncertainty (least possible error) is calculated as: $$\text{Uncertainty} = \frac{1}{2} \times (\text{Smallest scale division})$$

Step-by-Step Solution

1. Identify the smallest division: The smallest division on a metre rule is 1 mm.
2. Apply the uncertainty rule: The least possible error is half of the smallest division.
3. Calculate: $$\text{Error} = \frac{1 \text{ mm}}{2} = 0.5 \text{ mm}$$

Conclusion

The least possible error when using a metre rule is 0.5 mm. This represents the limit of precision for the instrument.

Exam Tip

Always remember the "Half-Division Rule" for analogue instruments:

• Metre Rule: Smallest division = 1 mm $\rightarrow$ Uncertainty = 0.5 mm.
• Vernier Caliper: Smallest division = 0.1 mm $\rightarrow$ Uncertainty = 0.05 mm.
• Micrometer Screw Gauge: Smallest division = 0.01 mm $\rightarrow$ Uncertainty = 0.005 mm.