Definition:Accuracy/Decimal Places

Definition

A representation $y$ in decimal notation of a number $x$ is:

accurate to $n$ decimal places

if and only if:

the number $n$ of digits after the decimal point of $x$ match the first $n$ digits after the decimal point of $y$, without rounding.

Examples

$\pi$ to $4$ Places

The constant pi ($\pi$) expressed accurate to $4$ decimal places is:

$\pi \approx 3 \cdotp 1415$

$e$ to $3$ Places

Euler's number $e$ expressed accurate to $3$ decimal places is:

$e \approx 2 \cdotp 718$

$e$ to $2$ Places

Euler's number $e$ expressed accurate to $2$ decimal places is:

$e \approx 2 \cdotp 72$

Root of $86.56$ to $2$ Places

The square root of $86 \cdotp 56$ expressed accurate to $2$ decimal places is:

$\sqrt {86 \cdotp 56} \approx 9 \cdotp 30$

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: 2. (accurate to $n$ decimal places)
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): correct to $n$ decimal places
• 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 $n$ decimal places
• 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 $n$ decimal places