Detailed Breakdown: Measurement & Uncertainty
Precision and Accuracy in Measurement: Accuracy reflects how close a measurement is to the true value, often limited by systematic errors (like a poorly calibrated balance). Precision describes the reproducibility of measurements, limited by random errors and the graduation of the instrument.
Propagation of Uncertainties: When raw data is used to calculate a result, the uncertainties must be combined. For addition and subtraction (e.g. calculating a change in temperature $\Delta T$), we sum the absolute uncertainties. For multiplication and division (e.g. calculating density), we sum the percentage uncertainties. This is critical for determining the reliability of experimental conclusions.
Significant Figures as a Reflection of Tool Precision: Significant figures represent all the certain digits in a measurement plus the first estimated digit. Calculations must respect these limits: results from addition/subtraction are limited by the least number of decimal places, while multiplication/division results are limited by the least number of significant figures.