Significant figures rules

Non-zero digits are always significant (123 -> 3 sig figs).
Zeros between non-zero digits are significant (1003 -> 4 sig figs).
Leading zeros are NOT significant (0.0042 -> 2 sig figs).
Trailing zeros after a decimal point ARE significant (1.500 -> 4 sig figs).
Trailing zeros in a whole number are ambiguous (2400 -> could be 2, 3, or 4); use scientific notation to clarify.

Arithmetic with sig figs

Multiplication/division: the result has as many sig figs as the factor with the fewest sig figs. (4.5 × 8.23 = 37, not 37.035)
Addition/subtraction: the result is rounded to the least number of decimal places. (12.11 + 3.1 = 15.2, not 15.21)

Scientific notation

Scientific notation makes sig figs unambiguous. 2.40 × 10³ has exactly 3 sig figs; 2.4 × 10³ has 2; 2.400 × 10³ has 4.

Common mistake examples

Number	Sig figs	Explanation
0.0042	2	Leading zeros are not significant; only 4 and 2 count
0.00420	3	Trailing zero after decimal is significant
2400	2 (ambiguous)	Trailing zeros in a whole number - use 2.400 × 10³ for 4 sig figs
2400.	4	Decimal point after trailing zeros makes them significant
100.0	4	All digits significant when decimal point is present

When significant figures matter most

Laboratory science: measurements have precision limits set by instruments; reporting more sig figs than the instrument provides is misleading.
Engineering calculations: a calculated answer is only as precise as the least precise input - over-reporting precision can create false confidence in tolerances.
Physics problems: significant figure rules are strictly enforced in physics coursework to build good habits for real-world measurement.

Exact numbers and counting numbers

Numbers obtained by counting (e.g., "3 apples") or defined constants (e.g., 1 inch = 2.54 cm exactly, or 1 dozen = 12) are exact - they have infinite significant figures and do not limit the sig figs of a calculation. If you multiply a measurement of 3.42 g by exactly 12 (one dozen), the result still has only 3 sig figs.