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![[parent]](http://images.planetmath.org:8080/images/uparrow.png)
decimal place
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(Definition)
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A decimal place of a number (a real number) $r$ is the position of a digit in its decimal expansion relative to the decimal point. Let us write $r$ as a decimal number:
$\xymatrix @C=0pt @H=10pt {A_nA_{n-1}\ldots A_1 & \bullet & D_1D_2\ldots D_m \ldots \\ & \save *\txt{the decimal point} \restore \ar[u] & }$
where each of the $A_i$ and $D_j$ is a digit in the decimal system (one of $0,1,2,3,4,5,6,7,8,9$ . In this decimal expansion,
- the $i$ th decimal place to the left of the decimal point is the position of $A_i$ and
- the $j$ th decimal place to the right of the decimal place is the position of $D_j$
The digits $A_i$ and $D_j$ are called the decimal place values. $A_i$ is the decimal place value corresponding to the $i$ th decimal place to the left of the decimal point, while $D_j$ is the decimal place value corresponding to the $j$ th decimal place to the right of the decimal point.
For decimal places closer to the decimal point, specific names are used. Below are some of the most commonly used names:
| name |
position from |
direction from |
example |
| |
the decimal point |
the decimal point |
(position of 7) |
| ones |
1st |
left |
$7.2$ |
| tens |
2nd |
left |
$71(=71.0)$ |
| hundreds |
3rd |
left |
$735(=735.0)$ |
| thousands |
4th |
left |
$7126(=7126.0)$ |
| tenths |
1st |
right |
$0.7$ |
| hundredths |
2nd |
right |
$12.47$ |
| thousandths |
3rd |
right |
$9.837$ |
| ten thousandths |
4th |
right |
$6.0037$ |
Remark. Instead of saying the $n$ th decimal place to the left or right of the decimal point, we simply say the $n$ th decimal place to mean the $n$ th decimal place to the right of the decimal point, and say $(-n)$ th decimal place to mean the $n$ th decimal place to the left of the decimal point.
For example, in $1632.9758$ the digit $5$ is located on the third decimal place, while $6$ is located on the negative third decimal place.
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"decimal place" is owned by CWoo. [ full author list (3) ]
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See Also: metric system
| Also defines: |
decimal place value, hundreds, thousands, tenths, hundredths, thousandths, ten thousandths |
This object's parent.
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Cross-references: negative, decimal number, decimal point, decimal expansion, digit, real number, number
There are 85 references to this entry.
This is version 9 of decimal place, born on 2007-08-08, modified 2008-10-16.
Object id is 9839, canonical name is DecimalPlace.
Accessed 17267 times total.
Classification:
| AMS MSC: | 00A05 (General :: General and miscellaneous specific topics :: General mathematics) |
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Pending Errata and Addenda
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