# Definition:Decimal Expansion/Decimal Point

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## Definition

Let $x \in \R$ have a decimal expansion:

- $n. d_1 d_2 d_3 \ldots$

The dot that separates the integer part from the fractional part of $x$ is called the **decimal point**.

That is, it is the radix point when used specifically for a base $10$ representation.

## Also denoted as

The usage of the **decimal point** varies between the various cultures.

The American system is to use a dot placed on the line:

- $12.345$

The British system is to place the dot centrally:

- $12 \cdotp 345$

The European system is to use a comma:

- $12, \! 345$

Consequently the thousands separator for European numbers is either a dot:

- $12.345, \! 678$

or a space:

- $12 \, 345, \! 678$

In $\mathsf{Pr} \infty \mathsf{fWiki}$ the British and American systems can be found for the **decimal point**, while the European usage of the space is generally used for the thousands separator.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $10$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $10$ - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $1$: Tokens, Tallies and Tablets: Symbols for small numbers - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $3$: Notations and Numbers: The Dark Ages?