Significant Figures/Ambiguous Presentation

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Warning

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.


Examples

Significant Figures of $186 \, 000 \, 000$

Consider the number $n$ presented as:

$n = 186 \, 000 \, 000$

It is impossible to tell exactly how many significant figures $n$ is presented to.

This could be any number from $3$ to $9$.


Suppose $n$ is presented to $5$ significant figures.

Then $n$ can be written in scientific notation as:

$n = 1 \cdotp 8600 \times 10^9$

and the matter is immediately clear.


If desired, $n$ can also be presented as:

$n = 168 \cdotp 00$ million


Sources

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