measurement uncertainty

Measurement uncertainty is the honest admission that no measurement is exact; every real reading has a range of doubt around it. When you measure a table as 1.20 m, you do not mean exactly 1.2000... m; you mean somewhere close to 1.20, give or take a little. Uncertainty is that 'give or take', written down as a number.

We report a result as best value plus-or-minus uncertainty, for example L = 1.20 plus-or-minus 0.01 m, meaning the true length very probably lies between 1.19 and 1.21 m. The uncertainty can come from the fineness of the instrument (a ruler marked in millimetres gives about plus-or-minus 0.5 mm) or from scatter when you repeat the measurement. When uncertain quantities are combined in a formula, their uncertainties propagate: roughly, for a sum you add the absolute uncertainties, and for a product you add the relative (percentage) uncertainties.

Stating uncertainty is not a sign of sloppiness; it is what makes a measurement scientific. A result with no uncertainty cannot be honestly compared with a theory or another experiment. This is why '12.3 plus-or-minus 0.1 cm' says far more than a bare '12.3 cm'.