Errors and Measurements

Accuracy tells us how close a measured value is to the true value, while precision tells us how closely repeated measurements agree with one another. JEE often uses this distinction in conceptual and assertion-reason questions.

The least count of an instrument is the smallest value it can resolve directly. Zero error must always be corrected before reporting the final reading. Repeated identical but wrong readings usually indicate systematic error; scattered readings around a mean indicate random error.

Significant figures encode the reliability of a measurement. In multiplication or division, the result keeps as many significant figures as the least precise factor. In addition or subtraction, the answer keeps the smallest decimal-place accuracy among the terms.

For a quantity $x$ with absolute error $\Delta x$:

In sums, absolute errors add. In products, quotients, and powers, relative errors add with powers acting as multipliers.