251:"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.
652:"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.
436:
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.
71:
53:
81:
22:
691:"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...
672:
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.
671:
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
632:
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
435:
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
527:
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
355:
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
272:
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.
609:
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.
295:
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)
371:
The
Knowledge 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.
729:) 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.
421:
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?
569:
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.
566:
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.
228:
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).
177:
303:
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. --
259:
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?
341:
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
633:
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).
757:
410:
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.
392:
This article offers opinions without clarifying that they are. I agree that significant arithmetic is a bit crazy, but isn't this an encyclopedia?
762:
395:
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.
591:
208:
103:
224:
The number of significant figures in the number "8" is actually infinite. The number "8." has only one significant figure.
94:
58:
33:
579:
The limitations of significant figures (also entirely ignored by this article) are discussed in extensive detail here:
615:
464:
I changed the uncertainty section a bit to try to reduce (ha ha) the uncertainty it likely introduces in the reader.
573:
Something coming close to significance arithmetic, using things like standard deviation, is briefly treated here:
696:
677:
657:
638:
377:
361:
204:
595:
21:
440:
692:
673:
653:
634:
611:
533:
469:
373:
200:
147:
39:
335:
100, 110 are significant up to the ones place, even though these digits are zeroes. So will the answer.
196:
740:
722:
707:
520:
357:
102:
on
Knowledge. If you would like to participate, please visit the project page, where you can join
552:
401:
547:
In colloquial
English, "error" is a synonym for a mistake. Let's try to avoid that usage here.
488:
345:
I changed 210 to 200, added an example that does add to 210, and clarified some of the prose.
714:
529:
465:
411:
260:
453:
was simpler, clearer, and more helpful than this one. I think it should be brought back.
523:" (or "significant digits") would like both the (relevant) information from that article,
454:
346:
70:
52:
737:
733:
283:
86:
751:
586:
574:
548:
304:
287:
274:
743:
700:
681:
661:
642:
619:
599:
556:
537:
508:
505:
498:
495:
473:
457:
443:
426:
423:
404:
381:
365:
349:
324:
The part about adding and subtracting sig figs is wrong at the part where it says:
307:
290:
277:
263:
80:
141:
How many sig. figs. are allowed in the result of the following mixed calculation?
580:
229:
76:
243:
Remember, 8., 8, and 08 all have one significant figure, wherease 8.0 has 2.
726:
182:
Since 29 - 25 = 4, is the quotient 7.2/4 entitled to only one sig. fig.?
99:
667:
Multiplying by numbers with infinite (or almost) significant digits.
494:
I'd be interested to know what that was, but the link is dead. --
300:
629:
The article says that 9.9 + 9.9 + 9.9 + 9.9 + 3.3 + 1.1 = 40.0
736:
change this article's title into a redirect to that section. –
286:
in a vacuum is defined to be 299,792,458 metres per second. --
15:
585:
This site includes the real meat of significance arithmetic.
727:§ Entire article ignores proper significance arithmetic
269:
I agree, the speed of light is definitely a bad example.
718:
450:
235:
So, technically, 8 x 8 is 64, whereas 8. x 8. is 60.
562:
Entire article ignores proper significance arithmetic
150:
98:, a collaborative effort to improve the coverage of
587:http://physics.nist.gov/cuu/Uncertainty/index.html
575:http://mathworld.wolfram.com/ErrorPropagation.html
171:
192:! --Methylene Blue 15:57, 9 November 2008 (UTC)
519:It seems to me that most people searching for "
504:It works for me. It should be put back in. --
8:
581:http://www.av8n.com/physics/uncertainty.htm
721:) that this article should be merged into
484:I removed the following from the article:
47:
151:
149:
32:does not require a rating on Knowledge's
725:, and I agree with the IP editor above (
49:
625:Addition using significance arithmetic
92:This redirect is within the scope of
19:
7:
719:§ Re-merge with Significant Figures?
172:{\displaystyle {\frac {7.2}{29-25}}}
706:This article should be merged into
38:It is of interest to the following
605:Usage of the Approximation Symbool
515:Re-merge with Significant Figures?
14:
723:Significant figures § Arithmetic
543:Using "error" to mean "mistake".
79:
69:
51:
20:
758:Redirect-Class science articles
763:NA-importance science articles
708:Significant figures#Arithmetic
405:23:05, 30 September 2006 (UTC)
278:19:31, 23 September 2005 (UTC)
220:Precise numbers vs. sig. fig.
1:
620:02:00, 17 November 2017 (UTC)
509:03:05, 20 December 2006 (UTC)
444:15:10, 11 December 2006 (UTC)
308:11:24, 17 November 2005 (UTC)
291:06:22, 17 November 2005 (UTC)
112:Knowledge:WikiProject Science
106:and see a list of open tasks.
600:08:11, 4 December 2008 (UTC)
538:16:12, 23 January 2008 (UTC)
499:16:42, 9 December 2006 (UTC)
474:17:20, 22 January 2008 (UTC)
427:16:50, 9 December 2006 (UTC)
115:Template:WikiProject Science
366:21:28, 5 October 2012 (UTC)
264:03:25, 31 August 2005 (UTC)
188:Yes, the answer being then
779:
744:02:06, 7 March 2024 (UTC)
717:'s post above from 2008 (
701:18:10, 11 July 2023 (UTC)
682:17:17, 11 July 2023 (UTC)
662:16:50, 11 July 2023 (UTC)
643:16:41, 11 July 2023 (UTC)
458:07:36, 31 July 2007 (UTC)
382:16:45, 11 July 2023 (UTC)
350:07:33, 31 July 2007 (UTC)
64:
46:
557:21:26, 5 June 2008 (UTC)
173:
320:100 has one sig. fig.
174:
148:
521:significant figures
95:WikiProject Science
713:I agree with the @
169:
137:Mixed Calculations
34:content assessment
612:Out of Phase User
414:1st November 2006
213:
199:comment added by
167:
134:
133:
130:
129:
126:
125:
770:
412:User:Winterstein
212:
193:
178:
176:
175:
170:
168:
166:
152:
120:
119:
118:science articles
116:
113:
110:
89:
84:
83:
73:
66:
65:
55:
48:
25:
24:
16:
778:
777:
773:
772:
771:
769:
768:
767:
748:
747:
711:
693:TheGoatOfSparta
689:
674:TheGoatOfSparta
669:
654:TheGoatOfSparta
650:
635:TheGoatOfSparta
627:
607:
564:
545:
517:
492:
482:
390:
374:TheGoatOfSparta
328:100 + 110 = 210
322:
257:
239:technically???!
222:
194:
156:
146:
145:
139:
117:
114:
111:
108:
107:
85:
78:
12:
11:
5:
776:
774:
766:
765:
760:
750:
749:
710:
704:
688:
685:
668:
665:
649:
646:
626:
623:
606:
603:
592:71.231.158.201
563:
560:
544:
541:
516:
513:
512:
511:
486:
481:
480:Broken link(s)
478:
477:
476:
461:
460:
438:
437:
432:
431:
430:
429:
416:
415:
389:
386:
385:
384:
358:DonaNobisPacem
353:
352:
339:
338:
337:
336:
330:
329:
321:
318:
317:
316:
315:
314:
313:
312:
311:
310:
284:speed of light
270:
256:
255:speed of light
253:
249:
248:
241:
240:
233:
232:
221:
218:
217:
216:
215:
214:
201:Methylene Blue
180:
179:
165:
162:
159:
155:
138:
135:
132:
131:
128:
127:
124:
123:
121:
104:the discussion
91:
90:
87:Science portal
74:
62:
61:
56:
44:
43:
37:
26:
13:
10:
9:
6:
4:
3:
2:
775:
764:
761:
759:
756:
755:
753:
746:
745:
742:
739:
735:
732:I'm going to
730:
728:
724:
720:
716:
709:
705:
703:
702:
698:
694:
687:Contradiction
686:
684:
683:
679:
675:
666:
664:
663:
659:
655:
647:
645:
644:
640:
636:
630:
624:
622:
621:
617:
613:
604:
602:
601:
597:
593:
589:
588:
583:
582:
577:
576:
571:
567:
561:
559:
558:
554:
550:
542:
540:
539:
535:
531:
526:
522:
514:
510:
507:
503:
502:
501:
500:
497:
490:
489:bean counting
485:
479:
475:
471:
467:
463:
462:
459:
456:
452:
448:
447:
446:
445:
442:
434:
433:
428:
425:
420:
419:
418:
417:
413:
409:
408:
407:
406:
403:
399:
396:
393:
387:
383:
379:
375:
370:
369:
368:
367:
363:
359:
351:
348:
344:
343:
342:
334:
333:
332:
331:
327:
326:
325:
319:
309:
306:
302:
298:
297:
294:
293:
292:
289:
285:
281:
280:
279:
276:
271:
268:
267:
266:
265:
262:
254:
252:
246:
245:
244:
238:
237:
236:
231:
227:
226:
225:
219:
210:
206:
202:
198:
191:
187:
186:
185:
184:
183:
163:
160:
157:
153:
144:
143:
142:
136:
122:
105:
101:
97:
96:
88:
82:
77:
75:
72:
68:
67:
63:
60:
57:
54:
50:
45:
41:
35:
31:
27:
23:
18:
17:
731:
715:Jon the Geek
712:
690:
670:
651:
631:
628:
608:
590:
584:
578:
572:
568:
565:
546:
530:Jon the Geek
528:objections?
524:
518:
493:
483:
466:Jon the Geek
449:I think the
439:
400:
397:
394:
391:
354:
340:
323:
258:
250:
242:
234:
223:
189:
181:
140:
93:
40:WikiProjects
29:
451:old article
441:ben.mcclure
261:Tejastheory
195:—Preceding
752:Categories
455:Redhookesb
347:Redhookesb
738:jacobolus
734:WP:BOLDly
648:Big words
487:example:
275:Mark Hurd
549:Bkalafut
398:Cheers,
305:Apoc2400
288:Apoc2400
209:contribs
197:unsigned
30:redirect
506:Djsonik
496:Slashme
424:Slashme
109:Science
100:Science
59:Science
402:Forezt
356:value.
36:scale.
301:metre
230:quota
28:This
697:talk
678:talk
658:talk
639:talk
616:talk
596:talk
553:talk
534:talk
525:plus
470:talk
388:rant
378:talk
362:talk
299:The
282:The
205:talk
741:(t)
247:OK.
154:7.2
754::
699:)
680:)
660:)
641:)
618:)
598:)
555:)
536:)
491:)
472:)
422:--
380:)
364:)
211:)
207:•
164:25
161:−
158:29
695:(
676:(
656:(
637:(
614:(
594:(
551:(
532:(
468:(
376:(
360:(
203:(
190:2
42::
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
