Science · Honors Chemistry
Chapter 1: Quantitative Foundations
Significant figures are an approximation to something exact.
Maya weighs a beaker holding a few drops of water at 25.03 g, then the dry beaker at 25.01 g, on a balance good to ±0.01 g. Each reading has four significant figures, and their difference, 0.02 ± 0.02 g, has none.
Where did the precision go?
Make your guess to turn the page.
Still to come: 10 pages · Lab · Words to Know · What We Learned · 4 questions · Explain It in Writing · Open Questions
The idea this lesson is working on — Students memorize the two significant-figure rules as unrelated conventions. The book derives both from how uncertainty propagates, then runs one pair of numbers through subtraction and multiplication in the lab. Ask: which uncertainty survives an addition, and which a multiplication? The idea to reach is that both rules shortcut one calculation.
Rayleigh and argon — Rayleigh reported the discrepancy in Nature in 1892 and in the Proceedings of the Royal Society in 1894. The masses here are rounded averages from his tables. Rayleigh and Ramsay announced argon in August 1894, and each received a Nobel Prize in 1904.
Worst case and root-sum-square — The lab’s widget adds uncertainties linearly, the worst case, which is what the significant-figure rules approximate. For independent random errors, statistics combines them in quadrature, which gives a smaller result. Either way the subtraction of close values is the case that fails.