Talk:Decimal fraction

Motivation[edit]

I got the idea for this page from the lengthy discussion on Talk:0.999... about the equality 0.999... = 1, and its proof. The length of this discussion results essentially from the fact that it involves an infinite decimal expansion, and such an infinite decimal cannot be defined correctly without the concept of limit, or, at least, if least upper bound of an infinite set, while this equality is frequently taught to kids who do not know these concepts. It is amazing that, although infinite decimals are a generalization of the more elementary finite decimals, nobody, except me, referred to finite decimals (in the discussion, and also in the article, before my edits).

So I have searched Wikipedia for finite decimals, and it appears that there is no article about this fundamental topic, widely used in all science, and in everyday use. Although only mathematicians are interested in infinite decimals, Decimal and all relative articles that I have found, emphasize one infinite numerals. I have not found any single article on the properties, usage and applications of finite decimals.

Thus I have decided to start this article, which should eventually include:

Operations on decimal numerals (management of decimal mark in the basic arithmetic operation)
Usage for approximating any number to a given precision (number of digits after the decimal mark)
The fact that decimal fractions are exactly the numbers that can be exactly represented by decimal numerals.
Some comments at the end on the generalization to infinite decimals.
...

When this will completed (or, maybe, before), the article should be moved to Decimal numeral. In fact the only interest of decimal fractions is to be the numbers that are exactly represented by decimal numerals. This project, when completed will eventually imply to restructure Decimal: One part of it and Decimal representation could become Infinite decimal or Decimal representation of real numbers. Another part would deserve to be merged with Hindu–Arabic numeral system. However it is too early for discussing this. D.Lazard (talk) 09:19, 7 August 2017 (UTC)[reply]

It is still not clear to me whether your topic is the numbers or the notation. If the numbers, then "decimal fraction", not "decimal numeral", is the right article. If the notation, then they should be included in the "decimal" article (the article about decimal notation), not turned into a separate WP:CONTENTFORK. As for your claim that this content was not already in the article: see Decimal#Decimal fractions. —David Eppstein (talk) 16:26, 7 August 2017 (UTC)[reply]

To editor David Eppstein: My intended topic was mainly about the numeral. I agree with you that this article should eventually included in Decimal. However, the present state of the article has many issues. The main ones:

The relationship between the decimal numeral system, the base-10 positional system and the Hindu-Arabic numeral system are not clearly stated. IMO, the two former are exactly the same, and are the extension to non-integer numbers of the latter, which generally refers only to the representation of the integers.
It is never said that repeating decimals and infinite decimals are not decimals (As a numeral system is aimed for representing (writing) numbers, an infinite string of symbols cannot be a numeral.
A large part of the content is out of scope (such that all comments about non-positional number systems and the fact that 10 is at the base of many of them) or should be moved near the bottom of the article as generalizations (everything that is related to infinite decimal expansion). In fact, the infinity is a difficult and technical concept, and its use almost from the beginning of the article make too technical an article that is supposed to be elementary.
In the large section "Decimal notation", only three or four lines are really devoted to decimal notation.

Fixing this issues cannot been done without important edits, and, in such an article, would lead to numerous reverts and endless discussions on the talk page. Nevertheless, thinking about your comment, I am now convinced that it is better to proceed more smoothly and to edit Decimal step after step. D.Lazard (talk) 10:24, 8 August 2017 (UTC)[reply]