Calculate, estimate, or predict an unknown quantity from known quantities by selecting and following a logical computational pathway and attending to precision.
Balances. A triple-beam balance reads to ±0.01 g; an analytical balance to ±0.0001 g. Tare (zero) the balance with the container in place, or weigh by difference: mass of container + sample, minus mass of container.
Significant figure rules:
Precision vs. accuracy: precision is reproducibility (how close repeated measurements are to one another); accuracy is closeness to the true value. A miscalibrated balance gives precise but inaccurate results.
Random vs. systematic error:
AP questions asking "would this make the result too high or too low?" are always about systematic error — which is exactly why they have a determinate answer.
A student weighs a sample as 2.4531 g on an analytical balance and dissolves it in water measured with a graduated cylinder as 50. mL. To how many significant figures should the resulting molarity be reported?
Two significant figures.
The mass, 2.4531 g, carries five significant figures — excellent precision from the analytical balance. But the volume, 50. mL, carries only two (the decimal point after the zero indicates it is significant; without it there would be ambiguity).
Molarity = moles ÷ litres is a division, so the result is limited by the least precise factor. The volume's two significant figures dominate, and the answer must be reported to two significant figures.
Practical lesson: the precision of an experiment is set by its weakest measurement. Using an analytical balance alongside a graduated cylinder wastes the balance's precision entirely — a volumetric flask should have been used.