significant digits

The number of leading digits in an approximation that are actually trustworthy, once the relative error is small enough.

An approximation $\tilde{x}$ is said to agree with the exact value $x$ to $n$ significant digits if $n$ is the largest integer for which $\dfrac{|x-\tilde{x}|}{|x|} \le 5\times10^{-n}$ .

Examples

3.14159 agrees with $\pi$ to 6 significant digits; 3.14 agrees with $\pi$ to only 3.