Chapter 2 · Measurement and Problem Solving
2.3Significant Figures: Writing Numbers to Reflect Precision
12 min · two checks
Predict
Do 0.00052 and 5.2 × 10⁻⁴ have the same number of significant figures?
The idea
- Count significant figures, including tricky zeros.
- Distinguish exact counted numbers from measured numbers.
A significant figure is a digit that carries measurement information. Nonzero digits always count. Zeros between nonzero digits count (captive zeros): 506 has three significant figures. Leading zeros never count: 0.0052 has two. Trailing zeros count only when a decimal point is written: 1500 has an ambiguous two to four, while 1.500 × 10³ has four and 1500. has four. Scientific notation is the clean way to show trailing zeros.
Exact numbers do not limit a calculation. There are exactly 100 cm in 1 m by definition, and a count of 12 beakers is exact if you truly counted them. A reading from a balance or a ruler is measured and carries uncertainty in the last digit you write. Report a measured value so that the last digit is the first uncertain one — no more, no fewer.
Keep these
- Leading zeros are not significant. Captive zeros are.
- Trailing zeros are significant when a decimal point is shown.
- Defined conversions and honest counts are exact and have no uncertainty of their own.