Radix point

In mathematics and computing, a radix point (or radix character) is a symbol used to separate whole numbers (integers) from fractions. For example, the number $1200.25$ represents the integer 1200 with a fractional part of 25, or 1200 and a fourth.

Because we use the decimal system, you probably know this point as the decimal point. "Decimal point" is a name specific to decimal, while "radix point" is a general name that can be used for any number system. Other number systems can have unique names too, like "binary point" for binary.

Most countries use either the period (.) or the comma (,) for the radix point. Some countries use them both in different contexts, such as Canada which uses periods in English and commas in French. A few countries use the Arabic decimal separator (٫).

Examples

In mathematical notation, each column of numbers represents a power of the radix, with a radix point noting the beginning of negative powers. For example, the base 10 number $1234.56$ is read as follows:

Powers	$10^{3}$	$10^{2}$	$10^{1}$	$10^{0}$	$10^{-1}$	$10^{-2}$
Value	1	2	3	4	5	6

Hence, we can unwrap the representation as this:

{\begin{aligned}&(1\times 10^{3})+(2\times 10^{2})+(3\times 10^{1})+(4\times 10^{0})+(5\times 10^{-1})+(6\times 10^{-2})\\&(1\times 1000)+(2\times 100)+(3\times 10)+(4\times 1)+(5\times 0.1)+(6\times 0.01)\\&1000+200+30+4+0.5+0.06\\&1234.56\end{aligned}}

To the left of the radix point is the integer part, made from positive powers. To the right of the radix point is the fractional part, made from negative powers.

Related pages

References