# 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**