Talk:Scientific notation

Fortran

In Fortran, I recall that their exponential notation sometimes uses a 'd' instead of 'e'. For example, a number might be written as 1.234d-4 meaning the same thing as 1.234 * 10^-4 . I could have been incorrectly informed, but I think this would be a nice note on this page if someone can find a source for it (I looked quickly, but didn't find anything). Fresheneesz 04:10, 15 September 2006 (UTC)

From the Nastran 77 Standard (http://www.fortran.com/F77_std/rjcnf-4.html#sh-4.5)

4.5.1 Double Precision Exponent.

The form of a double precision exponent is the letter D followed by an optionally signed integer constant. A double precision exponent denotes a power of ten. Note that the form and interpretation of a double precision exponent are identical to those of a real exponent, except that the letter D is used instead of the letter E.

Nastran uses the letter D to denote double precision instead of the single precision (or float) data type. Thus, this is an artifact of Nastran syntax. Jebix

As well as I know, E notation originated in Fortran, starting with Fortran I. (And no lower case, so E and not e.) Fortran, starting from the beginning, used formatting with FORMAT statements, and was given a sign and two digits. Some might put space, others plus, I might have forgotten, but the column is there. When systems allowed for three digit exponents, you got three digits and no +. For output, E or D was used, for REAL and DOUBLE PRECISION, respectively. (Double precision came with Fortran II, not so much later.) On input, either E or D worked. For program constants, E or D set the type of the constant. Gah4 (talk) 00:32, 31 March 2026 (UTC)

Isn't that backwards?

(Normalized) scientific notation is often called exponential notation...

AFAIK, "exponential notation" is generic, while "scientific notation" specifically refers to the one normalized so that the mantissa is in [1, 10), and "engineering notation" to the one normalized so that the mantissa is in [1, 1000) and the exponent is an integer multiple of three. Is that correct? --Army1987 (talk) 13:02, 9 June 2008 (UTC)

You are correct. The confusion arises because number notation is for many people the only place where they have to deal with exponents in any form or shape. 2A01:CB0C:CD:D800:D70:DD23:D4C0:C7E7 (talk) 09:42, 21 March 2021 (UTC)

Link Deletion —Preceding unsigned comment added by 86.17.229.118 (talk) 23:36, 6 November 2008 (UTC)

pt:Discussão:Notação científica

Fortran, back to the beginning, formats output with 0 digits before the decimal point, unless P is used. I believe it was still called scientific notation, though maybe Fortran notation would have made sense. Gah4 (talk) 00:35, 31 March 2026 (UTC)

E, D, and Q

As well as I know, E notation goes back to Fortran I, and D (for double precision) to Fortran II. The IBM 360/85 supports quad precision (S/360 format) hexadecimal notation, with the REAL*16 data type and Q constants and format descriptor. With VAX, DEC supported (but rare in hardware) H-float, as a 128 bit floating point type, using IBM's REAL*16 and Q constants and format descriptor. Gah4 (talk) 20:50, 5 May 2025 (UTC)

Are you asking for a change to the article? If so, please be specific about what you think should be changed and present "reliable sources" attesting to whatever change you want to see. (Feel free to directly make changes to the article, if you have reliable sources supporting them.) –jacobolus (t) 00:08, 6 May 2025 (UTC)

Seems that Q is there, and looks fine to me. Gah4 (talk) 00:51, 31 March 2026 (UTC)

E+ notation

Most spreadsheets use an E+ notation for large numbers (e.g. 1.2E+34, rather than 1.2E34), as well as some other computer programs. Is there any reason this isn't included in the E notation section? --Yodin^T 14:03, 24 March 2026 (UTC)

34 and +34 are the same number. Some calculators show the sign explicitly. Most don't. Headbomb {t · c · p · b} 15:32, 24 March 2026 (UTC)

Why are calculators more significant than computer programs? As I mentioned, almost all spreadsheets do use this form, as do several of the programming languages mentioned (C, JavaScript). I'm not suggesting that we replace all instances of E## with E+##, just that the E+ style is also mentioned. --Yodin^T 15:40, 24 March 2026 (UTC)

In the same way, you could argue that E and e are the same letter, but both are currently documented in the article, because the format of the notation is important, especially when the entire purpose of the article is to describe the notation. --Yodin^T 15:45, 24 March 2026 (UTC)

Fortran, and I suspect other languages, uses a fixed number of columns for the exponent. So, it is either blank space or + between the E and exponent. There are complications with having no separator, depending on where the file goes next. in Fortran for the IBM 704, first Fortran manual, the examples have blank space. Might see what the Fortran standard has in different years. Gah4 (talk) 01:01, 31 March 2026 (UTC)

It seems that by Fortran 77, the sign, + or -, is required in the exponent field. Unless the exponent width is specified in the FORMAT statement, four character positions are used. In the usual case, it is E+dd, or E-dd, but for exponents up to 999, or down to -999, it is Eddd or -ddd. That is, in the latter case, the E is left out. Gah4 (talk) 01:15, 31 March 2026 (UTC)

Trailing Significant Zero Digits in Scientific Notation

The discussion and examples of trailing significant zero digits in scientific notation is presented as an aside after discussing the topic itself. A zero being significant or insignificant is fundamental. None of the examples presented at the beginning of the discussions have trailing significant zero digits and the discussion of those examples implies that any such zero can be ignored. ~2026-20286-62 (talk) 17:27, 1 April 2026 (UTC)

The portion in the article discussing significant figures and trailing zeros (the only inclusion I see of the word "trailing" in the article) does seem to cover trailing zeros and their importance in scientific notation. Which portion of the article are you referring to when you say None of the examples presented at the beginning of the discussions have trailing significant zero digits? Jiltedsquirrel 🌰 ^{(talk || contribs)} 17:31, 1 April 2026 (UTC)

Those would be the eight examples in the table on the first page under

"scientific notation". ~2026-20286-62 (talk) 00:21, 2 April 2026 (UTC)

@2026-20286-62: Because there is no portion of that table that states the number of significant figures, I think it could be confusing to add an example with significant trailing zeros without additional explanation. Since this article is not primarily about significant figures, I am not excited about the idea of adding another column to the table at the top of the article to list the number of significant figures, but it is an option.

Decimal notation	Scientific notation
6720000000	6.72×109
6720000000	6.720×109

To me, the new example of 6.720E9 looks weird without additional address, because for someone who does not have a handle on significant figures and scientific notation, I think it may then appear as though for a value of 6,720,000,000 that there are many multiple correct ways to write the scientific notation: 6.72E9, 6.720E9, 6.7200E9, and so on. Do you have a better suggestion of how to go about making this clear in the top of the article? Jiltedsquirrel 🌰 ^{(talk || contribs)} 01:54, 2 April 2026 (UTC)

In order to correctly learn about scientific notation, the reader of this article must first know about significant digits/figures. The introduction of this article should refer the reader to the "Significant Figures" article. The remainder of the article needs to be rewritten to eliminate any implication or suggestion that all trailing zeros can be regarded as insignificant. ~2026-20286-62 (talk) 17:27, 2 April 2026 (UTC)

I suppose what I mean is: are there any specific suggestions about how to change the lead section to address significant figures? As I read it, the article as a whole does not state that trailing zeros are always insignificant, because trailing zeros are addressed within the significant figures section. Yes of course the trailing zeros can be significant, in which case it would be correct to include them in scientific notation for the number but they are not assumed to be significant without additional context. Jiltedsquirrel 🌰 ^{(talk || contribs)} 20:32, 2 April 2026 (UTC)

There are multiple correct ways to write this number in scientific notation, but the additional zeros are meaningful, and more than just the number per se is being communicated; some concept of the uncertainty associated with the quantity is also included in the expression. –jacobolus (t) 20:22, 2 April 2026 (UTC)

The section § Significant figures already explains this. –jacobolus (t) 20:24, 2 April 2026 (UTC)

What is important here is that scientific notation is a way of writing a number that conveys only those digit(s)/figure(s) that are significant. If the reader of this article does not already understand significant digits, they will not understand scientific notation after reading the earliest parts of this article. Reading about significant digits later in the article with different examples will likely cause the reader to presume that there are two different ways to use scientific notation: omit insignificant trailing zero digits or omit all trailing zero digits (as conveyed in each of the examples in the earliest parts of this article). ~2026-20286-62 (talk) 00:33, 3 April 2026 (UTC)

That's not really the primary point or most salient feature of scientific notation. Feel free to add ~ one sentence about it to the lead though. –jacobolus (t) 02:39, 3 April 2026 (UTC)

"Scientific notation is also a way of writing a multitude or magnitude number without having to include insignificant trailing zeros, i.e., using this notation, each conveyed digit in a number is significant" ~2026-20286-62 (talk) 04:07, 3 April 2026 (UTC)

Notes