Definition:Decimal Expansion/Decimal Point
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.
Also known as
Some (mainly historical) sources refer to the decimal point as the decimal dot.
Also see
- Results about the decimal point can be found here.
Sources
- 1938: A. Geary, H.V. Lowry and H.A. Hayden: Mathematics for Technical Students, Part One ... (previous) ... (next): Arithmetic: Chapter $\text I$: Decimals
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $10$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $10$
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): decimal point
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): decimal point
- 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?