Significant figures

Significant figures are the digits in a number that carry meaningful information about its precision and accuracy. In Numerical analysis and experimental science, they represent the reliable digits we actually know, plus one estimated digit.

When you measure something—a length, a temperature, a chemical concentration—your instrument has limits. A ruler marked in millimeters can't tell you about micrometers. Significant figures capture this reality: the number 5.20 cm has three significant figures and implies precision to the nearest 0.01 cm, while 5.2 cm has two and is less precise.

The rules seem fussy (leading zeros don't count, trailing zeros after a decimal point do), but they're essential for Error propagation. When you multiply or divide measurements, your answer can't be more precise than your least precise input. When you add or subtract, you're limited by the least precise decimal place.

Scientists and engineers use significant figures to communicate honestly about uncertainty. A bridge's load capacity stated as 500 tons versus 500.0 tons tells different stories. Climate data, medical dosages, Planetary observations—anywhere precision matters, significant figures prevent false confidence in unreliable digits.

Related

Measurement, Uncertainty principle, Data analysis, Rounding, Scientific notation