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:

$\pi \approx 3 \cdotp 1416$

$e$ to $4$ Figures

The Euler's number $e$ expressed accurate to $4$ significant figures is:

$e \approx 2 \cdotp 718$

$e$ to $3$ Figures

The Euler's number $e$ expressed accurate to $3$ significant figures is:

$e \approx 2 \cdotp 72$

$e^{-3}$ to $3$ Figures

$e^{-3} expressed accurate to $3$ significant figures is:

$e^{-3} \approx 0 \cdotp 0498$

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)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): accuracy
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): accurate (correct) to $n$ significant figures
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): accuracy
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): accurate (correct) to $n$ significant figures