significant figures
/ sig-NIF-ih-kunt FIG-yurz /
When you read a ruler that is only marked every centimetre, you can honestly say something is 'about 7.3 cm' — the 7 you are sure of, the .3 you are estimating — but writing 7.3149 cm would be a lie, because the ruler simply cannot tell you that much. Significant figures are the digits in a number that you actually have the right to claim: the ones you measured plus the single one you reasonably estimated. They are a quiet promise about how good your number really is.
More precisely, the significant figures of a measurement are all its certain digits together with the first uncertain (estimated) digit. Rules tell you which zeros count: zeros between non-zero digits always count (305 has three), trailing zeros after a decimal point count (2.50 has three), but leading zeros never count (0.0042 has two). When you multiply or divide, the answer keeps as many significant figures as the least precise input; when you add or subtract, you keep digits only as far right as the least precise place.
Significant figures matter because they communicate precision without writing out a full uncertainty statement — they are a shorthand for 'this is how much of this number you should trust.' The honest caveat is that they are only a rough convention: they cannot capture uncertainty exactly, and for careful work an explicit uncertainty (plus-or-minus a value) is better. Still, reporting too many digits overstates your confidence, and reporting too few throws away real information.
You weigh a sample as 1.2 g and dissolve it in exactly 100.00 mL. The concentration is 1.2 ÷ 0.10000 = 12 g/L — reported to two significant figures, not 12.000, because the limiting input (1.2 g) had only two.
The weakest measurement caps how precise the answer may look.
Exact counts and defined constants (like 100 items, or 1000 mL per L) have unlimited significant figures and never limit the result.