Significant Figures/Ambiguous Presentation
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
- 1972: Murray R. Spiegel and R.W. Boxer: Theory and Problems of Statistics (SI ed.) ... (previous) ... (next): Chapter $1$: Significant Figures
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): significant figures