In more detail
The rules: non-zero digits are significant; zeros between them are significant; leading zeros are not; trailing zeros after a decimal point are. So 0.00340 has three significant figures, and 1200 may have two to four depending on whether the zeros were measured; writing 1.20 × 10³ removes the doubt. Exact numbers, such as counts or defined conversions (1 inch = 2.54 cm), have unlimited precision and never limit a result.
Why it matters
A calculator shows every digit it can, which suggests precision the measurements do not have. For multiplication and division, report a result with no more significant figures than your least precise input. For addition and subtraction, the rule is about decimal places instead: keep the fewest decimal places. Round once at the end, not at every step. Software can hide meaningful zeros too: Python's .3g format drops trailing zeros, while #.3g keeps them.
Example
3.0 × 4.567 = 13.701 → 14 (3.0 has 2 sig figs)
9.81 × 2.5 = 24.525 → 25 (2.5 has 2 sig figs)
12.11 + 0.3 = 12.41 → 12.4 (0.3 has 1 decimal place)
>>> f"{0.00340:.3g}", f"{0.00340:#.3g}"
('0.0034', '0.00340')
Common confusion
Significant figures are not decimal places: 0.0034 has four decimal places but two significant figures. Scientific notation makes the count explicit.