2975:
574:
Until recently, the rule at the
International Organization for Standardization (ISO—the world's largest developer of standards) and the International Electrotechnical Commission (IEC—the leading global electrical and electronic standards organization) was that all numbers with a decimal part must be
318:
Numbers consisting of long sequences of digits can be made more readable by separating them into groups, preferably groups of three, separated by a small space. For this reason, ISO 31-0 specifies that such groups of digits should never be separated by a comma or point, as these are reserved for use
268:
articles for the list of standard symbols defined by the
International System of Units. The distinction between uppercase and lowercase letters is significant for SI unit symbols. For example, "k" is the prefix kilo and "K" stands for the unit kelvin. The symbols of all SI units named after a person
135:
is expressed here. Both the numerical value and the unit symbol are factors, and their product is the quantity. A quantity itself has no inherent particular numerical value or unit; as with any product, there are many different combinations of numerical value and unit that lead to the same quantity
147:
The value of a quantity is independent of the unit chosen to represent it. It must be distinguished from the numerical value of the quantity that occurs when the quantity is expressed in a particular unit. The above curly-bracket notation could be extended with a unit-symbol index to clarify this
412:. The sign for multiplying numbers is a cross (×) or a half-height dot (⋅). The cross should be used adjacent to numbers if a dot on the line is used as the decimal separator, to avoid confusion between a decimal dot and a multiplication dot.
466:. Numerator or denominator can themselves be products or quotients, but in this case, a solidus (/) should not be followed by a multiplication sign or division sign on the same line, unless parentheses are used to avoid ambiguity.
2301:
186:
This is a particularly useful and widely used notation for labelling the axes of graphs or for the headings of table columns, where repeating the unit after each numerical value can be typographically inconvenient.
164:= 698.2. In practice, where it is necessary to refer to the numerical value of a quantity expressed in a particular unit, it is notationally more convenient to simply divide the quantity through that unit, as in
356:
The only exceptions are the symbols for the units of plane angle: degree, minute of arc, and second of arc – which follow the numerical value without a space in between ("30 degrees" is expressed by "30°", for
73:
Physical quantities can be grouped into mutually comparable categories. For example, length, width, diameter and wavelength are all in the same category, that is they are all
1813:
440:
1808:
65:
used for the quantitative description of physical phenomena. The presentation here is a summary of some of the detailed guidelines and examples given in the standard.
101:" is the symbol for the physical quantity (wavelength), "m" is the symbol for the unit (metre), and "6.982 × 10" is the numerical value of the wavelength in metres.
1313:
691:
654:
593:
23:
1535:
269:
or a place start with an uppercase letter, as do the symbols of all prefixes from mega on upwards. All other symbols are lowercase; the only exception is
305:
2610:
2530:
2321:
2316:
2162:
2328:
349:
Numerical value and unit symbol are separated by a space. This rule also applies to the symbol "°C" for degrees
Celsius, as in "25 °C", and to the
682:
551:
575:
written in formal documents with a comma decimal separator, the prevailing fashion in Europe. The constant pi, for example, starts 3,141 592 653.
41:. It was intended for use in all fields of science and technology and is augmented by more specialized conventions defined in other parts of the
2861:
1223:
607:
2930:
2731:
2254:
1637:
1228:
1198:
336:
The multiplication sign is either a cross or a half-height dot, though the latter should not be used when the dot is the decimal separator.
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1905:
1702:
626:
1026:
214:
A subscript is only set in italic type if it consists of a symbol for a quantity or a variable. Other subscripts are set in upright (
2102:
1126:
362:
Where quantities are added or subtracted, parenthesis can be used to distribute a unit symbol over several numerical values, as in
2666:
1838:
1682:
81:, and then all other quantities in the same category can be expressed in terms of this unit, multiplied by a number called the
2761:
2756:
2463:
37:. It provides guidelines for using physical quantities, quantity and unit symbols, and coherent unit systems, especially the
273:, where both l and L are allowed. However, it is stated that the CIPM will examine whether one of the two may be suppressed.
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1885:
1818:
1398:
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3004:
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675:
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2177:
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709:
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1970:
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1955:
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1455:
889:
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264:
If an internationally standardized symbol exists for a unit, then only that symbol should be used. See the
201:
Quantities are generally represented by a symbol formed from single letters of the Latin or Greek alphabet.
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2746:
2736:
1865:
1283:
864:
668:
589:
2167:
2030:
1677:
1051:
899:
869:
762:
752:
713:
705:
475:
A comprehensive list of internationally standardized mathematical symbols and notations can be found in
561:
211:
If in a text different quantities use the same letter symbol, they can be distinguished via subscripts.
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2224:
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1338:
1121:
418:
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62:
304:
is either the comma on the line or the point on the line". This follows resolution 10 of the 22nd
2711:
2646:
986:
617:
1540:
77:. One particular example of such a quantity can be chosen as a reference quantity, called the
30:
225:
for a "nominal volume" (where "n" is just an abbreviation for the word "nominal"), but write
2274:
2015:
1343:
2999:
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2605:
2510:
2264:
2192:
2187:
2182:
1667:
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1625:
1620:
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1610:
1605:
1600:
333:
For numbers whose magnitude is less than 1, the decimal sign should be preceded by a zero.
254:
647:. NIST Special Publication 811. US National Institute of Standards and Technology, 2008.
640:. NIST Special Publication 330. US National Institute of Standards and Technology, 2008.
2172:
1920:
1732:
1595:
1585:
1580:
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1570:
1565:
1560:
1555:
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919:
909:
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644:
552:" Brief reference to the history | Decimals Score a Point on International Standards "
2993:
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2157:
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2142:
2020:
1965:
1940:
1935:
1915:
1788:
1328:
904:
767:
737:
50:
34:
2821:
2791:
2651:
1995:
1990:
1853:
1848:
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350:
301:
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1984:
956:
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205:
46:
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2137:
2092:
1828:
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2005:
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1980:
1950:
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1692:
1413:
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944:
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929:
837:
832:
827:
822:
508:
503:
476:
258:
49:. Other parts of ISO 31 have also been withdrawn and replaced by parts of
45:
standard. ISO 31-0 was withdrawn on 17 November 2009. It is superseded by
2590:
2368:
2072:
1900:
1737:
1727:
1712:
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599:
493:
346:
Unit symbols follow the numerical value in the expression of a quantity.
313:
For example, one divided by two (one half) may be written as 0.5 or 0,5.
2879:
2671:
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Unit rules and style conventions – Check list for reviewing manuscripts
531:
612:, Interdivisional Committee on Terminology, Nomenclature and Symbols (
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42:
26:
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On the use of italic and roman fonts for symbols in scientific text
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2010:
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556:
664:
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1652:
592:
ISO 31-0: Quantities and units — Part 0: General principles.
645:
498:
265:
246:
38:
629:. Interdivisional Committee on Nomenclature and Symbols,
144:} and notations useless, unless they are used together.
208:, independent of the type used in the rest of the text.
140:= 300 ⋅ m = 0.3 ⋅ km = ...). This ambiguity makes the {
421:
324:
For example, one million (1000000) may be written as
2893:
2619:
1771:
720:
276:
Symbols for units should be printed in an upright (
434:
131:, and represents the corresponding unit in which
300:ISO 31-0 (after Amendment 2) specifies that "the
536:22nd General Conference on Weights and Measures
655:National Institute of Standards and Technology
594:International Organization for Standardization
676:
8:
602:. Bureau International des Poids et Mesures.
683:
669:
661:
422:
420:
368:= 25 °C − 3 °C = (25 − 3) °C
523:
638:The International System of Units (SI)
293:Numbers should be printed in upright (
7:
289:See Sect. 3.3 of the Standard text.
127:} symbolizes the numerical value of
625:I. M. Mills and W. V. Metanomski:
550:Baum, Michael (22 November 2006).
204:Symbols for quantities are set in
14:
123:is the symbol for the quantity, {
16:Standardized quantities and units
2974:
2973:
450:, or by writing the product of
643:A. Thompson and B. N. Taylor:
636:B. N. Taylor and A. Thompson:
471:Mathematical signs and symbols
435:{\displaystyle {\frac {a}{b}}}
374:= 100 kW ± 5 kW = (100 ± 5) kW
156:= 6.982 × 10 or equivalently {
1:
104:More generally, we can write
22:is the introductory part of
606:Cvitas, T (February 2002),
415:Division can be written as
388:Products can be written as
241:Names and symbols for units
218:) type. For example, write
85:. For example, if we write
75:quantities of the same kind
3021:
244:
236:is a running index number.
2969:
702:
191:Typographic conventions
590:International standard
436:
196:Symbols for quantities
24:international standard
437:
377:(but not: 100 ± 5 kW)
353:, as in "10 %".
326:1 000 000
419:
319:as the decimal sign.
69:Quantities and units
564:on 27 November 2006
148:dependency, as in {
63:physical quantities
3005:1992 introductions
696:by standard number
432:
89:the wavelength is
2987:
2986:
710:ISO romanizations
616:), archived from
609:Quantity calculus
430:
383:= 12 × (1 ± 10) m
3012:
2977:
2976:
697:
685:
678:
671:
662:
633:, December 1999.
621:
578:
577:
571:
569:
560:. Archived from
547:
541:
539:
528:
441:
439:
438:
433:
431:
423:
327:
175:or equivalently
3020:
3019:
3015:
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3009:
2990:
2989:
2988:
2983:
2965:
2889:
2615:
1767:
716:
698:
695:
689:
605:
596:, Geneva, 1992.
586:
581:
567:
565:
549:
548:
544:
532:"Resolution 10"
530:
529:
525:
521:
485:
473:
417:
416:
343:
325:
287:
261:
255:SI derived unit
245:Main articles:
243:
230:
224:
198:
193:
171:/m = 6.982 × 10
163:
155:
83:numerical value
71:
59:
17:
12:
11:
5:
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2401:
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2175:
2170:
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2160:
2155:
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2140:
2135:
2130:
2125:
2120:
2115:
2110:
2105:
2100:
2095:
2090:
2085:
2080:
2075:
2070:
2065:
2060:
2055:
2050:
2049:
2048:
2043:
2033:
2028:
2023:
2018:
2013:
2008:
2003:
1998:
1993:
1988:
1978:
1973:
1968:
1963:
1958:
1953:
1948:
1943:
1938:
1933:
1928:
1923:
1918:
1913:
1908:
1903:
1898:
1893:
1888:
1883:
1878:
1873:
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1024:
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1014:
1009:
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994:
989:
984:
979:
974:
969:
964:
959:
954:
953:
952:
947:
942:
937:
932:
922:
917:
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907:
902:
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882:
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673:
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659:
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623:
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522:
520:
517:
516:
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501:
496:
491:
484:
481:
472:
469:
468:
467:
458:, for example
429:
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386:
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369:
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342:
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202:
197:
194:
192:
189:
184:
183:
173:
172:
161:
153:
117:
116:
95:
94:
93:= 6.982 × 10 m
70:
67:
61:ISO 31 covers
58:
55:
15:
13:
10:
9:
6:
4:
3:
2:
3017:
3006:
3003:
3001:
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2968:
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2810:
2808:
2805:
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729:
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723:
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714:IEC standards
711:
707:
706:ISO standards
701:
693:
686:
681:
679:
674:
672:
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666:
663:
656:
652:
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639:
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628:
624:
620:on 2005-04-04
619:
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56:
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40:
36:
32:
28:
25:
21:
2832:27000 series
777:
618:the original
608:
584:Bibliography
573:
566:. Retrieved
562:the original
555:
545:
535:
526:
474:
463:
459:
455:
451:
447:
443:
409:
405:
401:
397:
393:
389:
380:
371:
365:
351:percent sign
302:decimal sign
288:
251:SI base unit
233:
226:
219:
185:
182:/nm = 698.2.
179:
174:
168:
157:
149:
146:
141:
137:
132:
128:
124:
120:
118:
112:
108:
103:
98:
96:
90:
82:
78:
74:
72:
60:
19:
18:
2620:20000–29999
1772:10000–19999
600:SI brochure
568:17 November
513:ISO 80000-1
341:Expressions
280:) typeface.
206:italic type
47:ISO 80000-1
2994:Categories
2399:16949 (TS)
1996:11941 (TR)
694:standards
519:References
31:quantities
2354:15926 WIP
1718:9592/9593
1643:9000/9001
1531:8805/8806
509:ISO 80000
504:ISO 31-11
477:ISO 31-11
357:example).
259:SI prefix
51:ISO 80000
2979:Category
704:List of
494:ISO 1000
483:See also
20:ISO 31-0
2880:29199-2
2752:23094-2
2747:23094-1
2737:23090-3
2606:19794-5
2601:19775-1
2389:16612-2
2379:16355-1
2068:13406-2
2026:12234-2
1794:10118-3
657:, 1998.
308:, 2003.
297:) type.
285:Numbers
136:(e.g.,
3000:ISO 31
2894:30000+
1733:9797-1
1541:8820-5
1486:8501-1
1042:1073-2
1037:1073-1
721:1–9999
538:, BIPM
489:ISO 31
257:, and
119:where
97:then "
43:ISO 31
27:ISO 31
2961:80000
2956:56000
2951:55000
2946:50001
2941:45001
2936:42010
2931:40500
2926:39075
2921:38500
2916:37001
2911:32000
2906:31000
2901:30170
2885:29500
2875:29148
2871:29110
2867:28000
2862:27729
2857:27006
2852:27005
2847:27002
2842:27001
2837:27000
2827:26324
2822:26300
2817:26262
2812:26000
2807:25964
2802:25178
2797:24728
2792:24707
2787:24617
2782:24613
2777:24517
2772:23941
2767:23360
2762:23271
2757:23270
2742:23092
2732:23009
2727:23008
2722:23003
2717:23000
2712:22537
2707:22395
2702:22301
2697:22300
2692:22275
2687:22000
2682:21827
2677:21500
2672:21122
2667:21047
2662:21001
2657:21000
2652:20830
2647:20802
2642:20400
2637:20121
2632:20022
2627:20000
2611:19831
2596:19770
2591:19757
2586:19752
2581:19600
2576:19510
2571:19509
2566:19508
2561:19507
2556:19506
2551:19505
2546:19503
2541:19502
2536:19501
2531:19500
2526:19439
2521:19407
2516:19136
2511:19125
2506:19115
2501:19114
2484:19092
2479:19011
2474:19005
2469:18916
2464:18629
2459:18245
2454:18181
2449:18014
2444:18004
2439:17799
2434:17506
2429:17442
2424:17369
2419:17203
2414:17100
2409:17025
2404:17024
2394:16750
2384:16485
2374:16262
2369:16023
2364:15938
2359:15930
2349:15926
2344:15924
2339:15919
2334:15897
2329:15707
2317:15706
2312:15693
2307:15686
2302:15511
2297:15504
2292:15438
2287:15445
2270:15444
2265:15408
2260:15398
2255:15291
2250:15288
2245:15189
2240:15022
2235:14971
2230:14882
2225:14764
2220:14698
2215:14651
2210:14649
2205:14644
2200:14617
2148:14496
2143:14443
2138:14396
2133:14289
2128:14224
2123:14031
2118:14000
2113:13818
2108:13816
2103:13616
2098:13584
2093:13568
2088:13567
2083:13490
2078:13485
2073:13450
2063:13399
2058:13250
2053:13216
2036:13211
2031:12620
2021:12207
2016:12182
2011:12052
2006:12006
2001:11992
1991:11941
1981:11940
1976:11898
1971:11889
1966:11801
1961:11785
1956:11784
1951:11783
1946:11544
1941:11404
1936:11179
1931:11172
1926:11170
1921:11073
1916:10967
1911:10962
1906:10957
1901:10861
1896:10746
1891:10664
1886:10646
1881:10628
1876:10589
1871:10585
1866:10383
1834:10303
1829:10279
1824:10218
1819:10206
1814:10179
1809:10165
1804:10161
1799:10160
1789:10116
1784:10007
1779:10006
653:. US
631:IUPAC
614:IUPAC
404:, or
295:roman
278:roman
271:litre
216:roman
57:Scope
35:units
1859:-238
1763:9995
1758:9985
1753:9984
1748:9945
1743:9899
1738:9897
1728:9660
1723:9594
1713:9564
1708:9529
1703:9506
1698:9496
1693:9407
1688:9362
1683:9314
1678:9293
1673:9241
1668:9227
1663:9141
1658:9126
1653:9075
1648:9036
1638:8879
1591:-8-I
1546:8859
1536:8807
1526:8691
1521:8652
1516:8651
1511:8632
1506:8613
1501:8601
1496:8583
1491:8571
1481:8373
1476:8217
1471:8178
1466:8093
1461:8000
1456:7942
1451:7816
1446:7813
1441:7812
1436:7811
1431:7810
1426:7736
1421:7637
1409:7498
1404:7200
1399:7185
1394:7098
1389:7064
1384:7027
1379:7010
1374:7002
1369:7001
1364:6943
1359:6709
1354:6523
1349:6438
1344:6429
1339:6425
1334:6385
1329:6373
1324:6346
1319:6344
1314:6166
1309:5964
1304:5807
1299:5800
1294:5776
1289:5775
1284:5725
1279:5428
1274:5427
1269:5426
1264:5218
1259:4909
1254:4217
1249:4165
1244:4157
1239:4031
1234:3977
1229:3950
1224:3901
1219:3864
1214:3602
1209:3601
1204:3307
1199:3297
1177:3166
1172:3103
1167:3029
1162:2921
1157:2852
1152:2848
1147:2788
1142:2720
1137:2711
1132:2709
1127:2533
1122:2281
1117:2240
1112:2146
1107:2145
1102:2108
1097:2047
1092:2033
1087:2022
1082:2015
1077:2014
1072:1989
1067:1745
1062:1629
1057:1538
1052:1413
1047:1155
1032:1007
1027:1004
1022:1000
845:68-1
570:2018
557:NIST
454:and
306:CGPM
115:} ⋅
79:unit
33:and
2193:-20
2188:-17
2183:-14
2178:-12
2173:-11
2168:-10
1854:-28
1849:-22
1844:-21
1839:-11
1631:-16
1626:-15
1621:-14
1616:-13
1611:-12
1606:-11
1601:-10
1017:999
1012:965
1007:898
1002:860
997:843
992:838
987:764
982:732
977:704
972:690
967:668
962:657
957:646
925:639
920:519
915:518
910:500
905:361
900:306
895:302
890:262
885:261
880:259
875:233
870:228
865:226
860:217
855:216
850:128
838:-13
833:-12
828:-11
823:-10
692:ISO
394:a b
232:if
111:= {
29:on
2996::
2494:-2
2489:-1
2322:-2
2280:-9
2275:-3
2163:-6
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1192:-3
1187:-2
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152:}
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142:A
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