Definition:Significant Figures

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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 $n$.

In general the first non-zero digit, reading from left to right, is the first of the run of significant figures.


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.


Also see

  • Results about significant figures can be found here.


Sources

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