What is a significant figure?

Why should we be interested in significant figures?

In physics, a measurement is never perfect: it is always limited by the precision of the instrument. Writing too many or too few figures after a measurement gives a false impression of precision. Significant figures (often abbreviated to SF) are the digits in a number that convey real information about the measurement, excluding zeros that serve only to position the decimal point.

Rules for counting

• All non-zero digits are significant: 4.52 has 3 significant figures.
• Zeros placed between two non-zero digits are significant: 2.05 has 3 significant figures.
• Zeros to the left of the first non-zero digit are never significant: 0.0032 has 2 significant figures (only 3 and 2 count).
• Zeros to the right, after the decimal point, are significant: 3.40 has 3 significant figures (the final zero indicates precision to one hundredth).
• For an integer ending in zeros without a decimal point (e.g. 1500), the number of significant figures is ambiguous: scientific notation is preferred, for example 1.5 × 10³ (2 significant figures) or 1.500 × 10³ (4 significant figures).

Summary example

Value	Significant figures
7.0 cm	2
0.00450 kg	3
120 m (ambiguous)	2 or 3
1.20 × 10² m	3

Common pitfall

Do not confuse ‘significant figure’ with ‘digit after the decimal point’. The number 0.0025 has only 2 significant figures, even though it has 4 digits after the decimal point: leading zeros never count.