Measurement Uncertainties in Physics

Overview

This lecture introduces measurement uncertainties in physics, focusing on the definitions of uncertainty, accuracy, and precision, and covers methods for reporting and calculating uncertainties in measured and derived quantities.

Uncertainties in Measurement

• Uncertainty or error in physics is the likely maximum difference between a measured value and the true value.
• Measuring devices and methods inherently have limitations, causing uncertainties.

Accuracy vs. Precision

• Precision: Degree to which repeated measurements agree with each other.
• Accuracy: Closeness of a measurement to the accepted or true value.

Reporting Measurement Uncertainty

• Report a measured value as: value ± uncertainty (e.g., 2.51 ± 0.02 meters).
• The true value lies within the range [value − uncertainty, value + uncertainty].
• Shorthand notation writes the uncertainty's last digit in parentheses after the value (e.g., 2.51(2) meters for 0.02 uncertainty).

Percentage Uncertainty

• If uncertainty is given as a percentage, calculate uncertainty by multiplying the value by the percentage (e.g., 52 s ± 10% gives 5.2 s uncertainty).
• Range is [value − uncertainty, value + uncertainty].
• Report as: uncertainty in parentheses over the value (e.g., 5.2 s/52 s).

Calculating Uncertainty in Sums and Differences

• For two values with uncertainties, sum the measured values and add their uncertainties to get the total uncertainty.
• Example: (80 ± 1) g + (65 ± 2) g = 145 ± 3 g.
• For differences, subtract the measured values and use the same process for uncertainties (e.g., (80 ± 1) g − (65 ± 2) g = 15 ± 1 g).

Key Terms & Definitions

• Uncertainty (Error) — Maximum difference likely between a measured and the true value.
• Accuracy — How close a measurement is to the accepted or true value.
• Precision — How close repeated measurements are to each other.
• Uncertainty Notation — Reporting measured value followed by ± and the uncertainty (e.g., 2.51 ± 0.02 m).

Action Items / Next Steps

• Answer the pre-assessment and Unit 1 Activity 2 and 3 on page 4 of the assessment sheets.
• Read the “Propagation of Uncertainties” PDF file on your flash drive or scan the provided QR code for more resources.
• Reflect and write about dealing with uncertainties during the COVID-19 pandemic in the values integration section of your learning packet.