Talk:Significance arithmetic

Mixed Calculations
How many sig. figs. are allowed in the result of the following mixed calculation?
 * $$\frac{7.2}{29 - 25}$$

Since 29 - 25 = 4, is the quotient 7.2/4 entitled to only one sig. fig.?
 * Yes, the answer being then 2! --Methylene Blue 15:57, 9 November 2008 (UTC) —Preceding unsigned comment added by Methylene Blue (talk • contribs)

Precise numbers vs. sig. fig.
The number of significant figures in the number "8" is actually infinite. The number "8." has only one significant figure.


 * No, they both have just the one. A decimal point which is not followed by some other digit is irrelevant (especially in this font, where it might just be the period ending a sentence).  quota

So, technically, 8 x 8 is 64, whereas 8. x 8. is 60.


 * technically???!

Remember, 8., 8, and 08 all have one significant figure, wherease 8.0 has 2.


 * OK.

"8", by itself, doesn't have infinite significant figures. You need to know how that number was obtained -- if it was measured, then it has 1 significant figure, if it was counted, then it has an infinite number (if you want to call it that) of significant digits. The obtaining of the number is what's important -- i.e. If I counted 8 matches in each matchbook, and I counted that I have 8 matchbooks, then 8 * 8 = 64! However, if I measured that each candle is 8 cm (to 1 significant digit) long, then if I have 8 candles, 8 * 8 = 6 decimeter of candle, because I only know the measurement to 1 significant digit. When you have a counted number, it has no effect on the number of significant figures you carry. The use of the period after the number is only a convention.

speed of light
Is the speed of light really a defined physical constant with infinite significant figures? Isn't it simply a measured constant, and therefore have significant figures? Tejastheory 03:25, 31 August 2005 (UTC)


 * I agree, the speed of light is definitely a bad example.
 * Also Banker's rounding is most useful when the quantities are exact, but with just a few significant figures more than wanted, such as currency. Generally, a large number of values are more likely to average out any bias, so that's also a misleading statement. Mark Hurd 19:31, 23 September 2005 (UTC)
 * The speed of light in a vacuum is defined to be 299,792,458 metres per second. --Apoc2400 06:22, 17 November 2005 (UTC)
 * Speed of light is a constant, but it's still a measured constant. In a lot of physics, 3x10^8 is simply used, yet 3x10^8 does not have infinite significant figures - it is only precise to one significant figure. 07:03, 17 November 2005 (UTC)
 * The metre is defined as the length of the path travelled by light in absolute vacuum during a time interval of 1/299,792,458 of a second. So the speed of light is exactly 299,792,458 m/s. --Apoc2400 11:24, 17 November 2005 (UTC)

100 has one sig. fig.
The part about adding and subtracting sig figs is wrong at the part where it says:
 * 100 + 110 = 210
 * 100, 110 are significant up to the ones place, even though these digits are zeroes. So will the answer.

100 has 1 sig fig, and 110 has 2, therefore the answer would technically be 200. In order to do what they are saying you would have to do 1.00E2 + 1.10E2 = 2.10E2


 * I changed 210 to 200, added an example that does add to 210, and clarified some of the prose. Redhookesb 07:33, 31 July 2007 (UTC)

Looking back at my education, if I wanted to show 100 was significant to only one digit, it was written as 1x10^2; if I wrote 100, it was significant to the ones place value. None of my chemistry background included using a single decimal 100. to indicate it was significant to the ones place value.DonaNobisPacem (talk) 21:28, 5 October 2012 (UTC)


 * The Wikipedia article on significant figures says that 100 can have 1, 2, or 3 significant figures. It does not necessarily have 1 significant figure, so it should be specified, when one says/writes 100, how many significant figures it has. TheGoatOfSparta (talk) 16:45, 11 July 2023 (UTC)

rant
This article offers opinions without clarifying that they are. I agree that significant arithmetic is a bit crazy, but isn't this an encyclopedia?

Also, I'd like to suggest making a seperate article for significant digits instead of having it redirect here. I might do it if I have time.

Cheers,

Forezt 23:05, 30 September 2006 (UTC)


 * I agree. This article is a bit of rant. It would be better to have a clear concise explanation of signicance arithmetic with a note about problems. User:Winterstein 1st November 2006


 * I just noticed the comment above after redirecting the "significant figures" article here. It seems we've been around this same block very recently.  However, please explain why we need a separate article? --Slashme 16:50, 9 December 2006 (UTC)


 * Word. The inexplicably bitter tone of the now defunct entry on Significant Figures has now snuck into this otherwise promising page, under the "Uncertainty and Error" section. Significance arithmetic obviously has its limitations, but these limitations can certainly be addressed in a more measured tone. In addition, the section claims that "propagation of uncertainty" is the putative topic of the article. To the contrary, the article itself contains the text, "See the article on propagation of uncertainty for these more advanced and precise rules." It seems ungood to have an entry at variance with itself. This entry seems to need a unified explanation of the relationship between truly correct principles of uncertainty-reporting and all imperfect methods of uncertainty approximation. Right now, it's Correct Method Plus Some Approximation Methods on the one side, versus Evil Sig Figs on the other.

ben.mcclure 15:10, 11 December 2006 (UTC)


 * I think the old article was simpler, clearer, and more helpful than this one. I think it should be brought back.  Redhookesb 07:36, 31 July 2007 (UTC)


 * I changed the uncertainty section a bit to try to reduce (ha ha) the uncertainty it likely introduces in the reader. Jon the Geek (talk) 17:20, 22 January 2008 (UTC)

Broken link(s)
I removed the following from the article: example: bean counting)

I'd be interested to know what that was, but the link is dead. --Slashme 16:42, 9 December 2006 (UTC)


 * It works for me. It should be put back in. --Djsonik 03:05, 20 December 2006 (UTC)

Re-merge with Significant Figures?
It seems to me that most people searching for "significant figures" (or "significant digits") would like both the (relevant) information from that article, plus the information in this article. I plan to merge them together soon, with a substantial cleanup (and probably expansion), including pushing all of the (mostly beyond-the-scope of this article) dissenting views about the usefulness of sig figs into a section much like I did here yesterday. Any objections? Jon the Geek (talk) 16:12, 23 January 2008 (UTC)

Using "error" to mean "mistake".
In colloquial English, "error" is a synonym for a mistake. Let's try to avoid that usage here. Bkalafut (talk) 21:26, 5 June 2008 (UTC)

Entire article ignores proper significance arithmetic
The subject of this article is the usage of so-called "significant figures" or "digits" that are a crude and nebulous approximation to real significance arithmetic and error propagation.

Real significance arithmetic is the arithmetic of probability distributions. In this context, all measurements are considered as probability distributions, and arithmetic is performed on the distributions.

Something coming close to significance arithmetic, using things like standard deviation, is briefly treated here: http://mathworld.wolfram.com/ErrorPropagation.html

The limitations of significant figures (also entirely ignored by this article) are discussed in extensive detail here: http://www.av8n.com/physics/uncertainty.htm

This site includes the real meat of significance arithmetic. http://physics.nist.gov/cuu/Uncertainty/index.html

71.231.158.201 (talk) 08:11, 4 December 2008 (UTC)

Usage of the Approximation Symbool
Recent edits have replaced the "equals" symbol with the "approximation" symbol. Slightly pedantic, but I'm in the direction of agreeing. First time I've thought of this, though. Wanted to point it out, because I don't think it's completely irrelevant. Out of Phase User (talk) 02:00, 17 November 2017 (UTC)

Addition using significance arithmetic
The article says that 9.9 + 9.9 + 9.9 + 9.9 + 3.3 + 1.1 = 40.0

Shouldn't it be 44.0? "When adding or subtracting using significant figures rules, results are rounded to the position of the least significant digit in the most uncertain of the numbers being added" The result, before making any adjustments for significant figures, is 44 (exact). 44 (exact) rounded to the nearest tenth (position of the least significant digit in all of these numbers since they are equally uncertain) is 44.0 (44.00 rounds to 44.0). TheGoatOfSparta (talk) 16:41, 11 July 2023 (UTC)

Big words
"Significance arithmetic is a set of rules (sometimes called significant figure rules) for approximating the propagation of uncertainty in scientific or statistical calculations." I am not about to say that this should be removed, but it would be beneficial to add another sentence after it starting with "More simply..." or "In other words...", and explain it more easily. I don't see why I have to go read what propagation of uncertainty is when hundreds of textbooks explain significance arithmetic without introducing pointless big words. I am not complaining just about that sentence; there are many instances in this article where simpler explanations would be conducive to understanding.TheGoatOfSparta (talk) 16:50, 11 July 2023 (UTC)

Multiplying by numbers with infinite (or almost) significant digits.
Assume that I have to multiply a number whose finite digits are all significant by a number that has infinite or almost infinite significant digits (e.g. I have to multiply 2.31 by pi, where the three digits of 2.31 are all significant). How many digits of the number with infinite significant digits do I use (e.g do I multiply 2.31 by 3.14, 3.141, 3.1)? I think that you must use at least one more than the amount of digits that the number with finite digits has and that using more than that does not change the result (if you round). I am not sure about this though. I think this should be added to the article. TheGoatOfSparta (talk) 17:17, 11 July 2023 (UTC)

Contradiction
"So 6 × 10^1 is the best one can give, as other possible answers give a false sense of accuracy. Further, the 6 × 10^1 is itself confusing (as it might be considered to imply 60 ± 5, which is over-optimistic; more accurate would be 64 ± 8)." First it says it is the best answer and then it says it is confusing and there is a more accurate answer... TheGoatOfSparta (talk) 18:10, 11 July 2023 (UTC)

This article should be merged into Significant figures
I agree with the @Jon the Geek's post above from 2008 that this article should be merged into, and I agree with the IP editor above  that this subject of this article doesn't seem worthy of the title 'Significance arithmetic', which more commonly refers to (various) more serious scientific tools. Moreover, this current article is an unsourced mess.

I'm going to WP:BOLDly change this article's title into a redirect to that section. –jacobolus (t) 02:06, 7 March 2024 (UTC)