Measurement & Uncertainty Lab
Every measurement carries uncertainty. Learn to count significant figures, convert between units, propagate errors through calculations, and perform dimensional analysis with step-by-step conversion chains.
Guided Experiment: Significant Figures and Measurement Precision
How do trailing zeros, leading zeros, and decimal points affect the number of significant figures? Does the way you write a number change its implied precision?
Write your hypothesis in the Lab Report panel, then click Next.
Controls
Type the number exactly as written, including trailing zeros and decimal points
Results
- Leading zeros are never significant
- Trailing zeros after the decimal point are significant
Data Table
(0 rows)| # | Trial | Tab | Input | Output | Sig Figs | Uncertainty | Notes |
|---|
Reference Guide
Significant Figures
Significant figures communicate the precision of a measurement. Leading zeros are never significant, while trailing zeros after a decimal point always are.
A trailing decimal point (like 100.) makes all digits significant. Captive zeros between non-zero digits are always significant.
Unit Conversion
Multiply by conversion factors that equal 1 to change units without changing the value. The number of significant figures in the result matches the input.
Temperature conversions are special because they use offset formulas, not simple ratios.
Error Propagation
Uncertainties combine in quadrature. For addition and subtraction, add absolute uncertainties. For multiplication and division, add relative uncertainties.
For powers, the relative uncertainty is multiplied by the absolute value of the exponent.
Dimensional Analysis
Chain conversion factors so that unwanted units cancel, leaving only the desired unit. Each step multiplies by a fraction equal to 1.
If the units do not cancel correctly, the conversion chain has an error.