Measurement, Precision & Error
Grades 6+ Science Measurement
No measurement is ever exact. A ruler marked in millimeters can't tell you about micrometers; a bathroom scale can't weigh a postage stamp honestly. Science isn't pretending measurements are perfect — it's being honest about how imperfect they are. That honesty has rules.
Accuracy vs precision — not the same thing
- Accuracy: how close you are to the truth.
- Precision: how repeatable the measurement is.
A broken scale can be perfectly precise (same wrong answer every time) and a good scale can wobble a little (accurate on average). You want both, but they're independent properties.
Significant figures — digits that mean something
Writing "2.54 cm" claims you know three digits. Writing "2.54000 cm" claims a microscope. The digits you report are a promise about your instrument:
- Nonzero digits always count: 4.38 → 3 sig figs.
- Trapped zeros count: 20.07 → 4 sig figs.
- Trailing zeros after a decimal count: 3.500 → 4 sig figs (you're claiming that precision).
- Leading zeros never count: 0.0042 → 2 sig figs.
Error bars are a feature
Real scientists report "mass = 5.02 ± 0.03 g" — the ± isn't embarrassment, it's information. Two results can "disagree" on paper yet agree within uncertainty, and that distinction is how real experiments get judged.
- NIST (2008). Guide for the Use of the International System of Units (SP 811). National Institute of Standards and Technology. nist.gov/pml/special-publication-811 — the official US guide to writing measurements correctly.
- Taylor, J. R. (1997). An Introduction to Error Analysis. University Science Books. — the standard textbook on uncertainty; used in nearly every physics lab course.
- Mahajan, S. (2010). Street-Fighting Mathematics. MIT Press. free online — dimensional analysis: how units alone catch half of all calculation errors.
- How many sig figs in 0.003060? (4 — the trailing zero counts)
- Report 12.35 × 1.5 honestly (19 — two sig figs)
- Two scales read 100.1 g and 100.3 g ± 0.15 — do they disagree? (no — error bars overlap)
Related: scientific notation & SI · estimation · data & graphs.