Significant figures

A reported measurement should contain every digit known reliably plus the first uncertain digit; together these are the significant figures, and their number shows how precise the measurement was.

The precision depends on the least count of the instrument: 1.62 s has three significant figures (1 and 6 certain, 2 uncertain), 287.5 cm has four.

Changing the unit never changes the number of significant figures: 2.308 cm = 0.02308 m = 23.08 mm all have four.

All non-zero digits are significant, and zeros between two non-zero digits are significant wherever the decimal point is.

For a number less than 1, zeros after the decimal point but before the first non-zero digit are not significant; the zero written before the decimal point (as in 0.1250) is never significant.

Trailing zeros are significant in a number with a decimal point (3.500 and 0.06900 have four each) but not in a number without one (123 m = 12300 cm has three).

Scientific notation a × 10ᵇ with 1 ≤ a < 10 removes the ambiguity: 4.700 m = 4.700 × 10³ mm keeps its four significant figures, and every zero in a is significant.

For the order of magnitude, round a to 1 if a ≤ 5 and to 10 if 5 < a ≤ 10; the resulting power of ten is the order. The earth's diameter, 1.28 × 10⁷ m, is of order 10⁷ m; a hydrogen atom, 1.06 × 10⁻¹⁰ m, is of order 10⁻¹⁰ m, 17 orders smaller.

Exact numbers in a formula, such as the 2 in s = 2πr or a counted number of oscillations, have an unlimited number of significant figures.