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Significant figures

Significant figures are the digits in a number that carry real information about how precise the measurement is. Leading zeros do not count, while zeros between other digits and trailing zeros after the decimal point do. An answer can never be more precise than the numbers it was calculated from.

\text{Multiplying/dividing: fewest digits decide}

the answer is rounded to as many significant figures as the least precise factor

4.05 \to 3\ \text{digits}

zeros between digits count

0.0052 \to 2\ \text{digits}

leading zeros do not count

Symbols

$3.40$	3 significant figures (the trailing zero counts)
$0.004$	1 significant figure

Example

You calculate $2.5\ \mathrm{m}\cdot 3.142\ \mathrm{m}$ and the calculator shows $7.855$ . Since $2.5$ has the fewest digits (two), the answer is given as $7.9$ m².

Round off only at the very end of the calculation, never along the way.

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Part of Foundations of Physics: Quantities, units and measurement.