# Definition:Significant Figures

## Definition

Let $n$ be a number expressed in decimal notation.

The number of digits to which $n$ is rounded, apart from any digits needed to locate the decimal point, are referred to as the significant figures of $n$.

## Also known as

Significant figures are also known as significant digits.

## Examples

### Significant Figures of $64 \cdotp 4$

$64 \cdotp 4$ has $3$ significant figures.

### Significant Figures of $4 \cdotp 5300$

$4 \cdotp 5300$ has $5$ significant figures.

### Significant Figures of $0 \cdotp 0018$

$0 \cdotp 0018$ has $2$ significant figures.

### Significant Figures of $0 \cdotp 001800$

$0 \cdotp 001800$ has $4$ significant figures.

## Ambiguous Presentation

Consider a number $n$ which is reported to $d$ significant figures, but which is larger than $10^d$.

Then there will be one or more zero digits between the least significant digit and the decimal point.

Hence, when $n$ is written out in conventional notation, as a string of digits, it is not possible to determine by inspection exactly how many significant figures $n$ is being reported.

In order to avoid such ambiguity, it is recommended that such a number be expressed in scientific notation, as this then becomes clear.