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[parent] decimal place (Definition)

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 (2) ]
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Also defines:  decimal place value, hundreds, thousands, tenths, hundredths, thousandths, ten thousandths

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Cross-references: negative, decimal number, decimal point, decimal expansion, digit, real number
There are 65 references to this entry.

This is version 8 of decimal place, born on 2007-08-08, modified 2007-12-18.
Object id is 9839, canonical name is DecimalPlace.
Accessed 6101 times total.

Classification:
AMS MSC: 00A05 (General :: General and miscellaneous specific topics :: General mathematics)
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forum policy
autolinker issue by Wkbj79 on 2007-08-09 01:07:19
Because of the appearance of "ones", "tens", etc. in the defines list for this entry, the autolinker is linking the corresponding singulars to this entry as well. I tried to edit the linking policy to prevent this, but whenever I manage to prevent the singulars from linking, the plurals no longer link either. Can anything be done about this?
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