Editing Decimal (section)

== Decimal notation ==

For writing numbers, the decimal system uses ten [[decimal digit]]s, a [[decimal mark]], and, for [[negative number]]s, a [[minus sign]] "−". The decimal digits are [[0]], [[1]], [[2]], [[3]], [[4]], [[5]], [[6]], [[7]], [[8]], [[9]];<ref>In some countries, such as [[Arabic]]-speaking ones, other [[glyph]]s are used for the digits</ref> the [[decimal separator]] is the dot "{{math|.}}" in many countries (mostly English-speaking),<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Decimal|url=https://mathworld.wolfram.com/Decimal.html|access-date=2020-08-22|website=mathworld.wolfram.com|language=en|archive-date=2020-03-18|archive-url=https://web.archive.org/web/20200318204545/https://mathworld.wolfram.com/Decimal.html|url-status=live}}</ref> and a comma "{{math|,}}" in other countries.<ref name=":1" />

For representing a [[non-negative number]], a decimal numeral consists of
* either a (finite) sequence of digits (such as "2017"), where the entire sequence represents an integer:
*: <math>a_ma_{m-1}\ldots a_0</math>
* or a decimal mark separating two sequences of digits (such as "20.70828")
::<math>a_ma_{m-1}\ldots a_0.b_1b_2\ldots b_n</math>.
If {{math|''m'' > 0}}, that is, if the first sequence contains at least two digits, it is generally assumed that the first digit {{math|''a''<sub>''m''</sub>}} is not zero. In some circumstances it may be useful to have one or more 0's on the left; this does not change the value represented by the decimal: for example, {{math|1=3.14 = 03.14 = 003.14}}. Similarly, if the final digit on the right of the decimal mark is zero—that is, if {{math|1=''b''<sub>''n''</sub> = 0}}—it may be removed; conversely, trailing zeros may be added after the decimal mark without changing the represented number; {{NoteTag|text=Sometimes, the extra zeros are used for indicating the [[accuracy and precision|accuracy]] of a measurement. For example, "15.00&nbsp;m" may indicate that the measurement error is less than one centimetre (0.01&nbsp;m), while "15&nbsp;m" may mean that the length is roughly fifteen metres and that the error may exceed 10&nbsp;centimetres.}} for example, {{math|1=15 = 15.0 = 15.00}} and {{math|1=5.2 = 5.20 = 5.200}}.

For representing a [[negative number]], a minus sign is placed before {{math|''a''<sub>''m''</sub>}}.

The numeral <math>a_ma_{m-1}\ldots a_0.b_1b_2\ldots b_n</math> represents the number
:<math>a_m10^m+a_{m-1}10^{m-1}+\cdots+a_{0}10^0+\frac{b_1}{10^1}+\frac{b_2}{10^2}+\cdots+\frac{b_n}{10^n}</math>.
The ''[[integer part]]'' or ''integral part'' of a decimal numeral is the integer written to the left of the decimal separator (see also [[truncation]]). For a non-negative decimal numeral, it is the largest integer that is not greater than the decimal. The part from the decimal separator to the right is the ''[[fractional part]]'', which equals the difference between the numeral and its integer part.

When the integral part of a numeral is zero, it may occur, typically in [[computing]], that the integer part is not written (for example, {{math|.1234}}, instead of {{math|0.1234}}). In normal writing, this is generally avoided, because of the risk of confusion between the decimal mark and other punctuation.

In brief, the contribution of each digit to the value of a number depends on its position in the numeral. That is, the decimal system is a [[positional numeral system]].