Definition:Accuracy/Significant Figures

Definition

A representation $y$ in decimal notation of a number $x$ is accurate to $n$ significant figures if and only if the first $n$ digits of $x$ match, after rounding, the first $n$ digits of $y$.

In this context it is usual for $y$ to be expressed only by $n$ digits.

Examples

$\pi$ to $5$ Figures

The constant pi ($\pi$) expressed accurate to $5$ significant figures is:

$\pi \approx 3 \cdotp 1416$

Also known as

In the same way one can refer to a value as being accurate to $n$ decimal places or to $n$ significant figures, one can also say correct to $n$ decimal places or $n$ significant figures.

Also see

• Definition:Error

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): accurate or correct: 1. (accurate to $n$ significant digits)