Overview
This lecture explains how to measure length using the SI unit (meter), discusses measurement uncertainty, and provides examples for determining uncertainty in measurements.
SI Unit of Length
- The SI unit of length is the meter (m).
- Measurements of length are commonly made with rulers, tape measures, or other scaled instruments.
Measurement and Uncertainty
- All measurements using a scale have an inherent uncertainty.
- Uncertainty reflects the precision limit of the measuring instrument.
- The smallest marked division on the instrument defines the resolution of the measurement.
- To determine uncertainty: take half the value of the smallest division on your measuring scale.
- The unit of uncertainty matches the unit of the measurement (e.g., centimeters).
Example: Ruler with 0.1 cm Divisions
- If a ruler has 10 marks between each centimeter, the smallest division is 0.1 cm.
- Uncertainty for this ruler: 0.1 cm ÷ 2 = 0.05 cm.
- Example measurement: Object starts at 0 and ends at approximately 4.75 cm; report as 4.75 ± 0.05 cm.
- The last digit in the measurement is estimated.
Example: Ruler with 1 cm Divisions
- If a ruler only has marks for each whole centimeter, the smallest division is 1 cm.
- Uncertainty for this ruler: 1 cm ÷ 2 = 0.5 cm.
- Example measurement: Object is just over 3 cm, estimated at 3.1 ± 0.5 cm.
- Fewer marks mean less precise measurements and higher uncertainty.
Key Terms & Definitions
- Meter (m) — the SI unit of length.
- Uncertainty — half of the smallest scale division; represents the limit of precision for a measurement.
- Resolution — the smallest measurement increment a scale can show.
- Significant Digits — digits in a measurement known with certainty plus one estimated digit.
Action Items / Next Steps
- Watch the video "Why a Meter is a Meter."
- Practice measuring length and calculating uncertainty with rulers of different resolutions.