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.
Sources
- 1938: A. Geary, H.V. Lowry and H.A. Hayden: Mathematics for Technical Students, Part One ... (previous) ... (next): Arithmetic: Chapter $\text I$: Decimals: Decimal Places and Significant Figures
- 1972: Murray R. Spiegel and R.W. Boxer: Theory and Problems of Statistics (SI ed.) ... (previous) ... (next): Chapter $1$: Significant Figures
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): significant digits or significant figures
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): significant figures
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): significant figures
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): significant figures