1675:
system . Recognizing the advantage to be derived from the geometrical progression, he adopted a grading system that would yield a tenth multiple of the value after every fifth step of the series Renard's theory was to substitute more rounded but practical values as a power of 10, positive, nil or negative. He thus obtained 10 16 25 40 63 100 continued in both directions by the symbol R5 the R10, R20, R40 series were formed, each adopted ratio being the square root of the preceding one The first standardization drafts were drawn up on these bases in
Germany by the Normenausschuss der Deutschen Industrie on 13 April 1920, and in France by the Commission permanente de standardisation in document X of 19 December 1921. the commission of standardization in the Netherlands proposed their unification reached in 1931 in June 1932, the International Federation of the National Standardizing Associations organized an international meeting in Milan, where the ISA Technical Committee 32, Preferred numbers, was set up and its Secretariat assigned to France. On 19 September 1934, the ISA Technical Committee 32 held a meeting in Stockholm; sixteen nations were represented: Austria, Belgium, Czechoslovakia, Denmark, Finland, France, Germany, Hungary, Italy, Netherlands, Norway, Poland, Spain, Sweden, Switzerland, U.S.S.R. With the exception of the Spanish, Hungarian and Italian the other delegations accepted the draft Japan communicated its approval the international recommendation was laid down in ISA Bulletin 11 (December 1935). After the Second World War, the work was resumed by ISO. The Technical Committee ISO/TC 19, Preferred numbers, was set up and France again held the Secretariat. This Committee at its first meeting in Paris in July 1949 recommended preferred numbers defined by ISA Bulletin 11, R5, R10, R20, R40. This meeting was attended by 19 nations: Austria, Belgium, Czechoslovakia, Denmark, Finland, France, Hungary, India, Israel, Italy, Netherlands, Norway, Poland, Portugal, Sweden, Switzerland, United Kingdom, U.S.A., U.S.S.R. During subsequent meetings in New York in 1952 and the Hague in 1953, attended also by Germany, series R80 was added The draft thus amended became ISO Recommendation R3.
1410:, generating just 9 values of R10, just because of the kind of periodicity. This way rounding is eliminated, as the 3 values of the first period are repeated multiplied by 2. The usual cons however is that the thousand product of such multiplication is shifted slightly: Instead of decadic 1000, the binary 1024 appears, as classics in IT. The pro is that the characteristics is now fully valid, that whatever value multiplied by 2 is also member of the series, any rounding effectively eliminated. The multiplication by 2 is possible in R10 too, to get another members, but the long fractioned numbers complicate the R10 accuracy.
4279:
134:
usually rounded to a multiple of 0.05, and the R40 and R80 values interpolate between the R20 values, rather than being powers of the 80th root of 10 rounded correctly. In the table below, the additional R80 values are written to the right of the R40 values in the column named "R80 add'l". The R40 numbers 3.00 and 6.00 are higher than they "should" be by interpolation, in order to give rounder numbers.
133:
If a finer resolution is needed, another five numbers are added to the series, one after each of the original R5 numbers, and one ends up with the R10 series. These are rounded to a multiple of 0.05. Where an even finer grading is needed, the R20, R40, and R80 series can be applied. The R20 series is
1674:
Preferred numbers were first utilized in France at the end of the nineteenth century. From 1877 to 1879, Captain
Charles Renard, an officer in the engineer corps, made a rational study of the elements necessary in the construction of aircraft. He computed the specifications according to a grading
137:
In some applications more rounded values are desirable, either because the numbers from the normal series would imply an unrealistically high accuracy, or because an integer value is needed (e.g., the number of teeth in a gear). For these needs, more rounded versions of the Renard series have been
84:
If a set of nails with lengths between roughly 15 and 300 mm should be produced, then the application of the R5 series would lead to a product repertoire of 16 mm, 25 mm, 40 mm, 63 mm, 100 mm, 160 mm, and 250 mm long
65:
The most basic R5 series consists of these five rounded numbers, which are powers of the fifth root of 10, rounded to two digits. The Renard numbers are not always rounded to the closest three-digit number to the theoretical geometric sequence:
45:. The factor between two consecutive numbers in a Renard series is approximately constant (before rounding), namely the 5th, 10th, 20th, or 40th root of 10 (approximately 1.58, 1.26, 1.12, and 1.06, respectively), which leads to a
80:
If some design constraints were assumed so that two screws in a gadget should be placed between 32 mm and 55 mm apart, the resulting length would be 40 mm, because 4 is in the R5 series of preferred
1716:
3605:
1952:
Tuffentsammer, Karl (1956). "Das
Dezilog, eine Brücke zwischen Logarithmen, Dezibel, Neper und Normzahlen" [The decilog, a bridge between logarithms, decibel, neper and preferred numbers].
53:
is minimized if an arbitrary number is replaced by the nearest Renard number multiplied by the appropriate power of 10. One application of the Renard series of numbers is the current rating of
1385:
is the desired number of divisions within the major step size of twelve. Similarly, a base of two, eight, or sixteen would fit nicely with the binary units commonly found in computer science.
1396:
after a slash. For example, "R10″/3 (1…1000)" designates a series consisting of every third value in the R″10 series from 1 to 1000, that is, 1, 2, 4, 8, 15, 30, 60, 120, 250, 500, 1000.
1939:
Tuffentsammer, Karl; Schumacher, P. (1953). "Normzahlen – die einstellige
Logarithmentafel des Ingenieurs" [Preferred numbers - the engineer's single-digit logarithm table].
1366:. But one would need to use an appropriate number base to avoid ending up with two incompatible sets of nicely spaced dimensions, if for instance they were applied with both
1931:
ISO Recommendation R497-1966 - Preferred
Numbers - Guide to the Choice of Series of Preferred Numbers and of Series Containing More Rounded Values of Preferred Numbers
1399:
Such narrowing of the general original series brings the opposite idea of deepening the series and to redefine it by a strict simple formula. As the beginning of the
1703:
3117:
3112:
26:
dividing an interval from 1 to 10 into 5, 10, 20, or 40 steps. This set of preferred numbers was proposed ca. 1877 by French army engineer
Colonel
3334:
1830:
1795:
3122:
2617:
1995:
30:
and reportedly published in an 1886 instruction for balloon troops, thus receiving the current name in 1920s. His system was adopted by the
1780:
1403:
series seen higher, the {1, 2, 4, 8, ...} series can be defined as binary. That means that the R10 series can be formulated as R10 ≈ bR3 =
2839:
4313:
124:(252 gal., ca 954 liters) could have become 63 (or 60 by R″5), 100, 160 (or 150), 250, 400, 630 (or 600) and 1000 liters, respectively.
3809:
1908:
ISO 497:1973-05 - Guide to the choice of series of preferred numbers and of series containing more rounded values of preferred numbers
3914:
3834:
3625:
3620:
3466:
3632:
1986:
1785:
4165:
2355:
1536:]. Wissenschaftliche Normung (in German). Vol. 2 (reprint of 1st ed.). Berlin / Göttingen / Heidelberg, Germany:
138:
defined in ISO 3. In the table below, rounded values that differ from their less rounded counterparts are shown in bold.
2527:
1614:
1545:
57:. Another common use is the voltage rating of capacitors (e.g. 100 V, 160 V, 250 V, 400 V, 630 V).
4234:
4035:
3558:
2941:
2532:
2502:
1912:
1658:
1494:
1681:
ISO Recommendation R17-1956 - Preferred
Numbers - Guide to the Use of Preferred Numbers and of Series of Preferred Numbers
1583:
3879:
3209:
3006:
2330:
3406:
2430:
1354:
As the Renard numbers repeat after every 10-fold change of the scale, they are particularly well-suited for use with
1916:
1662:
1488:
3970:
3142:
2986:
1712:
4065:
4060:
3819:
3767:
3859:
3189:
2702:
2350:
1882:
1839:
1804:
1434:
4204:
3682:
1979:
1768:
1523:
4308:
3864:
3772:
3722:
3481:
2814:
2809:
2208:
4130:
4075:
3854:
3839:
3097:
2517:
2013:
1746:
4178:
4085:
3874:
3849:
3061:
3056:
1764:
3732:
3274:
3264:
3259:
2834:
2819:
2759:
2193:
2188:
2148:
89:
4282:
4050:
4040:
3169:
2587:
2168:
1972:
1873:
1424:
39:
1636:
3471:
2981:
2203:
2173:
2066:
2056:
2017:
2009:
1465:
4229:
4135:
3869:
3844:
3687:
3528:
3279:
2966:
2769:
2642:
2425:
1790:
8:
4070:
1654:
ISO 17:1973-04 - Guide to the use of preferred numbers and of series of preferred numbers
1537:
4015:
3950:
2290:
1859:
1734:
46:
2844:
1894:
1863:
1851:
1816:
1541:
1459:
1419:
54:
4303:
3578:
3319:
2647:
1964:
1886:
1843:
1808:
1638:
Mechanical
Engineering: The Journal of the American Society of Mechanical Engineers
23:
4188:
3909:
3814:
3568:
3496:
3491:
3486:
2971:
2934:
2929:
2924:
2919:
2914:
2909:
2904:
1610:
1527:
113:
3476:
3224:
3036:
2899:
2889:
2884:
2879:
2874:
2869:
2864:
2859:
2854:
2223:
2213:
1890:
1847:
1812:
1569:
50:
27:
4297:
4264:
4239:
4224:
4160:
4155:
4150:
4145:
4140:
3985:
3930:
3899:
3889:
3752:
3742:
3712:
3707:
3657:
3637:
3615:
3600:
3553:
3518:
3461:
3456:
3446:
3324:
3269:
3244:
3239:
3219:
3092:
2632:
1898:
1855:
1820:
105:
101:
1509:
ISO Recommendation R3-1954 - Preferred
Numbers - Series of Preferred Numbers
4125:
4095:
3955:
3299:
3294:
3157:
3152:
3147:
3066:
3011:
2961:
2894:
2849:
2824:
2754:
2749:
2744:
2739:
2734:
2692:
2657:
2567:
2562:
2390:
2198:
1429:
1374:. In the case of inches and feet a root of 12 would be desirable, that is,
4100:
3797:
3792:
3787:
3371:
3288:
2260:
1906:
1652:
1371:
117:
1576:
Logarithms, preferred numbers, decibel, neper, phon - naturally related!
1388:
Each of the Renard sequences can be reduced to a subset by taking every
4090:
3995:
3702:
3677:
3441:
3396:
3132:
2789:
2602:
2495:
2490:
2485:
2445:
2420:
2295:
2051:
1363:
1358:
units. It makes no difference whether the Renard numbers are used with
121:
4259:
4254:
4249:
4244:
4219:
4209:
4170:
4120:
4115:
4110:
4105:
4010:
4005:
4000:
3990:
3980:
3965:
3945:
3940:
3935:
3884:
3829:
3824:
3804:
3782:
3762:
3717:
3697:
3652:
3647:
3642:
3610:
3573:
3563:
3548:
3543:
3538:
3523:
3508:
3503:
3431:
3426:
3421:
3401:
3391:
3386:
3381:
3366:
3361:
3309:
3304:
3284:
3254:
3229:
3214:
3184:
3137:
3127:
3107:
3102:
3087:
3082:
2996:
2717:
2712:
2607:
2253:
2248:
2243:
2238:
2233:
2141:
2136:
2131:
2126:
1439:
3894:
3672:
3376:
3204:
3041:
3031:
3016:
2991:
2976:
2951:
2946:
2829:
2804:
2799:
2784:
2779:
2774:
2764:
2729:
2724:
2707:
2687:
2682:
2677:
2672:
2667:
2662:
2652:
2637:
2627:
2622:
2612:
2597:
2592:
2582:
2577:
2572:
2557:
2552:
2547:
2542:
2537:
2522:
2507:
2480:
2475:
2470:
2465:
2460:
2455:
2450:
2440:
2435:
2415:
2410:
2400:
2395:
2385:
2380:
2370:
2365:
2360:
2335:
2325:
2218:
2121:
2116:
2111:
2106:
2101:
2096:
2091:
2086:
2081:
1571:
Logarithmen, Normzahlen, Dezibel, Neper, Phon - natürlich verwandt!
109:
4183:
3975:
3960:
3757:
3747:
3737:
3513:
3329:
3174:
3162:
2320:
2315:
2310:
2305:
2300:
2285:
2280:
2275:
2270:
2265:
2228:
2183:
2178:
2163:
2158:
2153:
1444:
93:
4045:
4030:
4025:
4020:
3692:
3667:
3595:
3451:
3436:
3416:
3411:
3356:
3349:
3344:
3339:
3234:
3199:
3046:
2697:
2512:
2076:
1490:
ISO 3:1973-04 - Preferred
Numbers - Series of Preferred Numbers
1392:
th value in a series, which is designated by adding the number
97:
4080:
4055:
3777:
3662:
3533:
3314:
3179:
3051:
3026:
3021:
3001:
2375:
2345:
2340:
2061:
2046:
2036:
2031:
1449:
1359:
1688:
ISO R17/A1-1966 - Amendment 1 to ISO Recommendation R17-1955
3727:
3590:
3583:
3249:
3194:
2794:
2405:
1454:
1367:
1828:
Van Dyck, Arthur F. (February 1936). "Preferred Numbers".
38:, first published in 1953 or 1954, which evolved into the
4214:
3904:
2956:
31:
1871:
Van Dyck, Arthur F. (March 1951) . "Preferred Numbers".
1705:
U.S. Metric Study Interim Report - Engineering Standards
1938:
1355:
1715:(NBS). NBS Special Publication 345-11 (Code: XNBSA).
1994:
1635:Engineers, American Society of Mechanical (1924).
4295:
1831:Proceedings of the Institute of Radio Engineers
1796:Proceedings of the Institute of Radio Engineers
1695:
1763:
1526:(2013-10-04) . Written at Hannover, Germany.
1980:
1951:
1781:The American Society of Mechanical Engineers
1605:
1603:
1483:
1481:
1769:"Size Standardization by Preferred Numbers"
1641:. American Society of Mechanical Engineers.
1516:
1317:
1304:
1301:
1286:
1271:
1266:
1261:
1246:
1233:
1230:
1217:
1204:
1201:
1198:
1183:
1168:
1163:
1150:
1137:
1134:
1131:
1118:
1105:
1102:
1089:
1076:
1071:
1066:
1053:
1038:
1033:
1020:
1007:
1004:
1001:
952:
939:
936:
923:
910:
907:
894:
881:
878:
863:
848:
845:
826:
807:
802:
789:
774:
771:
752:
737:
734:
721:
708:
705:
692:
677:
674:
655:
640:
637:
579:
560:
557:
538:
519:
516:
513:
494:
475:
472:
453:
434:
431:
428:
409:
390:
387:
368:
349:
346:
343:
324:
305:
302:
283:
264:
261:
258:
239:
220:
217:
198:
179:
176:
173:
1987:
1973:
1645:
1561:
1789:
1701:
1634:
1600:
1478:
1870:
1827:
1522:
4296:
1793:(January 1927) . "Preferred Numbers".
1567:
1968:
128:
1913:International Standards Organization
1659:International Standards Organization
1495:International Standards Organization
141:
167:
90:traditional English wine cask sizes
13:
1757:
1702:De Simone, Daniel V. (July 1971).
14:
4325:
4314:Logarithmic scales of measurement
4278:
4277:
1941:Werkstattechnik und Maschinenbau
1713:The National Bureau of Standards
1919:from the original on 2017-11-02
1722:from the original on 2017-11-03
1665:from the original on 2017-11-02
1617:from the original on 2017-11-01
1589:from the original on 2016-12-18
1339:
1336:
1333:
1330:
1325:
1320:
1312:
1307:
1296:
1291:
1281:
1276:
1256:
1251:
1241:
1236:
1225:
1220:
1212:
1207:
1193:
1188:
1178:
1173:
1158:
1153:
1145:
1140:
1126:
1121:
1113:
1108:
1097:
1092:
1084:
1079:
1061:
1056:
1048:
1043:
1028:
1023:
1015:
1010:
996:
993:
990:
987:
971:
968:
965:
960:
955:
947:
942:
931:
926:
918:
913:
902:
897:
889:
884:
871:
866:
856:
851:
838:
831:
819:
812:
797:
792:
782:
777:
764:
757:
745:
740:
729:
724:
716:
711:
700:
695:
685:
680:
667:
660:
648:
643:
632:
629:
626:
610:
607:
604:
601:
598:
593:
590:
585:
582:
574:
571:
566:
563:
552:
549:
544:
541:
533:
530:
525:
522:
508:
505:
500:
497:
489:
486:
481:
478:
467:
464:
459:
456:
448:
445:
440:
437:
423:
420:
415:
412:
404:
401:
396:
393:
382:
379:
374:
371:
363:
360:
355:
352:
338:
335:
330:
327:
319:
316:
311:
308:
297:
294:
289:
286:
278:
275:
270:
267:
253:
250:
245:
242:
234:
231:
226:
223:
212:
209:
204:
201:
193:
190:
185:
182:
165:
162:
159:
156:
153:
1628:
120:(126 gal., ca 477 liters) and
60:
1:
1767:; Berry, C. H. (1922-12-04).
1471:
1883:Institute of Radio Engineers
1840:Institute of Radio Engineers
1805:Institute of Radio Engineers
1568:Paulin, Eugen (2007-09-01).
1435:E series (preferred numbers)
104:(31.5 gal., ca 119 liters),
70:R5: 1.00 1.60 2.50 4.00 6.30
7:
1613:. Sizes, Inc. 2014-06-10 .
1413:
74:
16:System of preferred numbers
10:
4330:
1891:10.1109/JRPROC.1951.230759
1848:10.1109/JRPROC.1936.228053
1813:10.1109/JRPROC.1926.221089
1329:
1316:
1300:
1285:
1260:
1245:
1229:
1216:
1197:
1182:
1162:
1149:
1130:
1117:
1101:
1088:
1065:
1052:
1032:
1019:
1000:
964:
951:
935:
922:
906:
893:
877:
862:
844:
825:
801:
788:
770:
763:
751:
733:
720:
704:
691:
673:
654:
636:
597:
578:
556:
537:
512:
493:
471:
452:
427:
408:
386:
367:
342:
334:
323:
301:
282:
257:
238:
216:
197:
172:
116:(84 gal., ca 318 liters),
112:(63 gal., ca 239 liters),
108:(42 gal., ca 159 liters),
4273:
4197:
3923:
3075:
2024:
2006:
1765:Hirshfeld, Clarence Floyd
982:
621:
148:
92:had been metricated, the
49:. This way, the maximum
1874:Proceedings of the IRE
1773:Mechanical Engineering
1425:Preferred metric sizes
40:international standard
1791:Hazeltine, Louis Alan
1779:(12). New York, USA:
1466:Geometric progression
36:ISO Recommendation R3
1524:Kienzle, Otto Helmut
34:in 1949 to form the
1711:. Washington, USA:
1661:(ISO). April 1973.
1611:"preferred numbers"
1538:Springer-Verlag OHG
2000:by standard number
129:Alternative series
47:geometric sequence
4309:Industrial design
4291:
4290:
2014:ISO romanizations
1915:(ISO). May 1973.
1547:978-3-642-99831-7
1534:Preferred numbers
1497:(ISO). April 1973
1460:Nominal Pipe Size
1420:Preferred numbers
1351:
1350:
1344:
1343:
976:
975:
615:
614:
169:
100:, ca 68 liters),
24:preferred numbers
4321:
4281:
4280:
2001:
1989:
1982:
1975:
1966:
1965:
1961:
1948:
1934:
1927:
1925:
1924:
1902:
1867:
1842:(IRE): 159–179.
1824:
1807:(IRE): 785–787.
1784:
1751:
1750:
1744:
1740:
1738:
1730:
1728:
1727:
1721:
1710:
1699:
1693:
1691:
1684:
1677:
1671:
1670:
1649:
1643:
1642:
1632:
1626:
1625:
1623:
1622:
1607:
1598:
1597:
1595:
1594:
1588:
1581:
1565:
1559:
1557:
1555:
1554:
1520:
1514:
1512:
1505:
1503:
1502:
1485:
1409:
1408:
1380:
1379:
980:
979:
619:
618:
146:
145:
142:
22:are a system of
4329:
4328:
4324:
4323:
4322:
4320:
4319:
4318:
4294:
4293:
4292:
4287:
4269:
4193:
3919:
3071:
2020:
2002:
1999:
1993:
1954:VDI-Zeitschrift
1929:
1922:
1920:
1905:
1760:
1758:Further reading
1755:
1754:
1742:
1741:
1732:
1731:
1725:
1723:
1719:
1708:
1700:
1696:
1686:
1679:
1668:
1666:
1651:
1650:
1646:
1633:
1629:
1620:
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149:least rounded
140:
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82:
76:
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62:
59:
55:electric fuses
51:relative error
28:Charles Renard
15:
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2574:
2571:
2569:
2566:
2564:
2561:
2559:
2556:
2554:
2551:
2549:
2546:
2544:
2541:
2539:
2536:
2534:
2531:
2529:
2526:
2524:
2521:
2519:
2516:
2514:
2511:
2509:
2506:
2504:
2501:
2497:
2494:
2492:
2489:
2487:
2484:
2483:
2482:
2479:
2477:
2474:
2472:
2469:
2467:
2464:
2462:
2459:
2457:
2454:
2452:
2449:
2447:
2444:
2442:
2439:
2437:
2434:
2432:
2429:
2427:
2424:
2422:
2419:
2417:
2414:
2412:
2409:
2407:
2404:
2402:
2399:
2397:
2394:
2392:
2389:
2387:
2384:
2382:
2379:
2377:
2374:
2372:
2369:
2367:
2364:
2362:
2359:
2357:
2354:
2352:
2349:
2347:
2344:
2342:
2339:
2337:
2334:
2332:
2329:
2327:
2324:
2322:
2319:
2317:
2314:
2312:
2309:
2307:
2304:
2302:
2299:
2297:
2294:
2292:
2289:
2287:
2284:
2282:
2279:
2277:
2274:
2272:
2269:
2267:
2264:
2262:
2259:
2255:
2252:
2250:
2247:
2245:
2242:
2240:
2237:
2235:
2232:
2231:
2230:
2227:
2225:
2222:
2220:
2217:
2215:
2212:
2210:
2207:
2205:
2202:
2200:
2197:
2195:
2192:
2190:
2187:
2185:
2182:
2180:
2177:
2175:
2172:
2170:
2167:
2165:
2162:
2160:
2157:
2155:
2152:
2150:
2147:
2143:
2140:
2138:
2135:
2133:
2130:
2128:
2125:
2123:
2120:
2118:
2115:
2113:
2110:
2108:
2105:
2103:
2100:
2098:
2095:
2093:
2090:
2088:
2085:
2083:
2080:
2079:
2078:
2075:
2073:
2070:
2068:
2065:
2063:
2060:
2058:
2055:
2053:
2050:
2048:
2045:
2043:
2040:
2038:
2035:
2033:
2030:
2029:
2027:
2023:
2019:
2018:IEC standards
2015:
2011:
2010:ISO standards
2005:
1997:
1990:
1985:
1983:
1978:
1976:
1971:
1970:
1967:
1959:
1956:(in German).
1955:
1950:
1946:
1943:(in German).
1942:
1937:
1932:
1918:
1914:
1910:
1909:
1904:
1900:
1896:
1892:
1888:
1884:
1880:
1876:
1875:
1869:
1865:
1861:
1857:
1853:
1849:
1845:
1841:
1837:
1833:
1832:
1826:
1822:
1818:
1814:
1810:
1806:
1802:
1798:
1797:
1792:
1788:
1786:
1782:
1778:
1774:
1770:
1766:
1762:
1761:
1748:
1736:
1718:
1714:
1707:
1706:
1698:
1689:
1682:
1676:
1664:
1660:
1656:
1655:
1648:
1640:
1639:
1631:
1616:
1612:
1606:
1604:
1585:
1582:(in German).
1577:
1573:
1572:
1564:
1549:
1543:
1539:
1535:
1531:
1530:
1525:
1519:
1510:
1496:
1492:
1491:
1484:
1482:
1477:
1467:
1464:
1461:
1458:
1456:
1453:
1451:
1448:
1446:
1443:
1441:
1438:
1436:
1433:
1431:
1428:
1426:
1423:
1421:
1418:
1417:
1411:
1402:
1397:
1395:
1391:
1386:
1384:
1373:
1369:
1365:
1361:
1357:
1347:
1324:
1311:
1295:
1289:
1280:
1274:
1269:
1264:
1255:
1249:
1240:
1224:
1211:
1192:
1186:
1177:
1171:
1166:
1157:
1144:
1125:
1112:
1096:
1083:
1074:
1069:
1060:
1047:
1041:
1036:
1027:
1014:
986:
983:most rounded
981:
978:
959:
946:
930:
917:
901:
888:
874:
870:
859:
855:
841:
837:
834:
829:
822:
818:
815:
810:
805:
796:
785:
781:
767:
760:
755:
748:
744:
728:
715:
699:
688:
684:
670:
666:
663:
658:
651:
647:
625:
620:
617:
589:
570:
548:
529:
504:
485:
463:
444:
419:
400:
378:
359:
315:
293:
274:
249:
230:
208:
189:
152:
147:
144:
143:
139:
135:
123:
119:
115:
111:
107:
103:
99:
95:
91:
87:
83:
79:
78:
69:
68:
67:
58:
56:
52:
48:
44:
41:
37:
33:
29:
25:
21:
20:Renard series
4136:27000 series
2071:
2041:
1957:
1953:
1944:
1940:
1930:
1921:. Retrieved
1907:
1885:(IRE): 115.
1878:
1872:
1835:
1829:
1800:
1794:
1776:
1772:
1724:. Retrieved
1704:
1697:
1687:
1680:
1673:
1667:. Retrieved
1653:
1647:
1637:
1630:
1619:. Retrieved
1591:. Retrieved
1575:
1570:
1563:
1551:. Retrieved
1533:
1528:
1518:
1513:(July 1953))
1511:. July 1954.
1508:
1499:. Retrieved
1489:
1430:1-2-5 series
1400:
1398:
1393:
1389:
1387:
1382:
1353:
1345:
1287:
1272:
1267:
1262:
1247:
1184:
1169:
1164:
1072:
1067:
1039:
1034:
872:
857:
839:
832:
827:
820:
813:
808:
803:
783:
765:
758:
753:
746:
686:
668:
661:
656:
649:
136:
132:
64:
42:
35:
19:
18:
3924:20000–29999
3076:10000–19999
1928:(Replaced:
1685:(1955) and
1678:(Replaced:
1558:(340 pages)
1506:(Replaced:
1364:millimetres
61:Base series
4298:Categories
3703:16949 (TS)
3300:11941 (TR)
1998:standards
1960:: 267–274.
1923:2017-11-02
1726:2017-11-03
1669:2017-11-02
1621:2017-11-01
1593:2016-12-18
1553:2017-11-01
1501:2016-12-18
1472:References
43:ISO 3
3658:15926 WIP
3022:9592/9593
2947:9000/9001
2835:8805/8806
1947:(4): 156.
1899:0096-8390
1864:140107818
1856:0731-5996
1821:0731-5996
1745:ignored (
1735:cite book
1440:Logarithm
4283:Category
2008:List of
1917:Archived
1717:Archived
1663:Archived
1615:Archived
1584:Archived
1414:See also
1401:selected
114:puncheon
110:hogshead
81:numbers.
75:Examples
4304:Numbers
4184:29199-2
4056:23094-2
4051:23094-1
4041:23090-3
3910:19794-5
3905:19775-1
3693:16612-2
3683:16355-1
3372:13406-2
3330:12234-2
3098:10118-3
1933:. 1966.
1783:: 791–.
1690:. 1966.
1683:. 1956.
1445:Decibel
1405:√
1376:√
98:gallons
94:rundlet
4198:30000+
3037:9797-1
2845:8820-5
2790:8501-1
2346:1073-2
2341:1073-1
2025:1–9999
1897:
1862:
1854:
1819:
1578:]
1544:
1381:where
1368:inches
1360:metres
1346:
106:tierce
102:barrel
85:nails.
4265:80000
4260:56000
4255:55000
4250:50001
4245:45001
4240:42010
4235:40500
4230:39075
4225:38500
4220:37001
4215:32000
4210:31000
4205:30170
4189:29500
4179:29148
4175:29110
4171:28000
4166:27729
4161:27006
4156:27005
4151:27002
4146:27001
4141:27000
4131:26324
4126:26300
4121:26262
4116:26000
4111:25964
4106:25178
4101:24728
4096:24707
4091:24617
4086:24613
4081:24517
4076:23941
4071:23360
4066:23271
4061:23270
4046:23092
4036:23009
4031:23008
4026:23003
4021:23000
4016:22537
4011:22395
4006:22301
4001:22300
3996:22275
3991:22000
3986:21827
3981:21500
3976:21122
3971:21047
3966:21001
3961:21000
3956:20830
3951:20802
3946:20400
3941:20121
3936:20022
3931:20000
3915:19831
3900:19770
3895:19757
3890:19752
3885:19600
3880:19510
3875:19509
3870:19508
3865:19507
3860:19506
3855:19505
3850:19503
3845:19502
3840:19501
3835:19500
3830:19439
3825:19407
3820:19136
3815:19125
3810:19115
3805:19114
3788:19092
3783:19011
3778:19005
3773:18916
3768:18629
3763:18245
3758:18181
3753:18014
3748:18004
3743:17799
3738:17506
3733:17442
3728:17369
3723:17203
3718:17100
3713:17025
3708:17024
3698:16750
3688:16485
3678:16262
3673:16023
3668:15938
3663:15930
3653:15926
3648:15924
3643:15919
3638:15897
3633:15707
3621:15706
3616:15693
3611:15686
3606:15511
3601:15504
3596:15438
3591:15445
3574:15444
3569:15408
3564:15398
3559:15291
3554:15288
3549:15189
3544:15022
3539:14971
3534:14882
3529:14764
3524:14698
3519:14651
3514:14649
3509:14644
3504:14617
3452:14496
3447:14443
3442:14396
3437:14289
3432:14224
3427:14031
3422:14000
3417:13818
3412:13816
3407:13616
3402:13584
3397:13568
3392:13567
3387:13490
3382:13485
3377:13450
3367:13399
3362:13250
3357:13216
3340:13211
3335:12620
3325:12207
3320:12182
3315:12052
3310:12006
3305:11992
3295:11941
3285:11940
3280:11898
3275:11889
3270:11801
3265:11785
3260:11784
3255:11783
3250:11544
3245:11404
3240:11179
3235:11172
3230:11170
3225:11073
3220:10967
3215:10962
3210:10957
3205:10861
3200:10746
3195:10664
3190:10646
3185:10628
3180:10589
3175:10585
3170:10383
3138:10303
3133:10279
3128:10218
3123:10206
3118:10179
3113:10165
3108:10161
3103:10160
3093:10116
3088:10007
3083:10006
1881:(2).
1860:S2CID
1838:(2).
1803:(4).
1720:(PDF)
1709:(PDF)
1587:(PDF)
1580:(PDF)
1574:[
1532:[
1462:(NPS)
1450:Neper
994:R″20
991:R″10
972:10.0
969:10.0
966:10.0
961:9.50
956:9.00
953:9.00
948:8.50
943:8.00
940:8.00
937:8.00
932:7.50
927:7.10
924:7.10
919:6.70
914:6.30
911:6.30
908:6.30
903:6.00
898:5.60
895:5.60
890:5.30
885:5.00
882:5.00
879:5.00
867:4.50
864:4.50
852:4.00
849:4.00
846:4.00
798:3.00
793:2.80
790:2.80
778:2.50
775:2.50
772:2.50
741:2.00
738:2.00
735:2.00
730:1.90
725:1.80
722:1.80
717:1.70
712:1.60
709:1.60
706:1.60
701:1.50
696:1.40
693:1.40
681:1.25
678:1.25
675:1.25
644:1.00
641:1.00
638:1.00
633:R′40
630:R′20
627:R′10
608:10.0
605:10.0
602:10.0
599:10.0
594:9.75
591:9.50
586:9.25
583:9.00
580:9.00
575:8.75
572:8.50
567:8.25
564:8.00
561:8.00
558:8.00
553:7.75
550:7.50
545:7.30
542:7.10
539:7.10
534:6.90
531:6.70
526:6.50
523:6.30
520:6.30
517:6.30
514:6.30
509:6.15
506:6.00
501:5.75
498:5.60
495:5.60
490:5.45
487:5.30
482:5.15
479:5.00
476:5.00
473:5.00
468:4.87
465:4.75
460:4.62
457:4.50
454:4.50
449:4.37
446:4.25
441:4.12
438:4.00
435:4.00
432:4.00
429:4.00
424:3.87
421:3.75
416:3.65
413:3.55
410:3.55
405:3.45
402:3.35
397:3.25
394:3.15
391:3.15
388:3.15
383:3.07
380:3.00
375:2.90
372:2.80
369:2.80
364:2.72
361:2.65
356:2.58
353:2.50
350:2.50
347:2.50
344:2.50
339:2.43
336:2.36
331:2.30
328:2.24
325:2.24
320:2.18
317:2.12
312:2.06
309:2.00
306:2.00
303:2.00
298:1.95
295:1.90
290:1.85
287:1.80
284:1.80
279:1.75
276:1.70
271:1.65
268:1.60
265:1.60
262:1.60
259:1.60
254:1.55
251:1.50
246:1.45
243:1.40
240:1.40
235:1.36
232:1.32
227:1.28
224:1.25
221:1.25
218:1.25
213:1.22
210:1.18
205:1.15
202:1.12
199:1.12
194:1.09
191:1.06
186:1.03
183:1.00
180:1.00
177:1.00
174:1.00
168:add'l
3163:-238
3067:9995
3062:9985
3057:9984
3052:9945
3047:9899
3042:9897
3032:9660
3027:9594
3017:9564
3012:9529
3007:9506
3002:9496
2997:9407
2992:9362
2987:9314
2982:9293
2977:9241
2972:9227
2967:9141
2962:9126
2957:9075
2952:9036
2942:8879
2895:-8-I
2850:8859
2840:8807
2830:8691
2825:8652
2820:8651
2815:8632
2810:8613
2805:8601
2800:8583
2795:8571
2785:8373
2780:8217
2775:8178
2770:8093
2765:8000
2760:7942
2755:7816
2750:7813
2745:7812
2740:7811
2735:7810
2730:7736
2725:7637
2713:7498
2708:7200
2703:7185
2698:7098
2693:7064
2688:7027
2683:7010
2678:7002
2673:7001
2668:6943
2663:6709
2658:6523
2653:6438
2648:6429
2643:6425
2638:6385
2633:6373
2628:6346
2623:6344
2618:6166
2613:5964
2608:5807
2603:5800
2598:5776
2593:5775
2588:5725
2583:5428
2578:5427
2573:5426
2568:5218
2563:4909
2558:4217
2553:4165
2548:4157
2543:4031
2538:3977
2533:3950
2528:3901
2523:3864
2518:3602
2513:3601
2508:3307
2503:3297
2481:3166
2476:3103
2471:3029
2466:2921
2461:2852
2456:2848
2451:2788
2446:2720
2441:2711
2436:2709
2431:2533
2426:2281
2421:2240
2416:2146
2411:2145
2406:2108
2401:2047
2396:2033
2391:2022
2386:2015
2381:2014
2376:1989
2371:1745
2366:1629
2361:1538
2356:1413
2351:1155
2336:1007
2331:1004
2326:1000
2149:68-1
1895:ISSN
1852:ISSN
1817:ISSN
1747:help
1542:ISBN
1455:Phon
1372:feet
1370:and
1318:9.0
1305:8.0
1302:8.0
1234:5.0
1231:5.0
1218:4.5
1205:4.0
1202:4.0
1199:4.0
1151:2.8
1138:2.5
1135:2.5
1132:2.5
1119:2.2
1106:2.0
1103:2.0
1090:1.8
1077:1.6
1054:1.4
1021:1.1
1008:1.0
1005:1.0
1002:1.0
988:R″5
873:4.80
858:4.20
840:3.80
833:3.60
828:3.60
821:3.40
814:3.20
809:3.20
804:3.20
784:2.60
766:2.40
759:2.20
754:2.20
747:2.10
687:1.30
669:1.20
662:1.10
657:1.10
650:1.05
166:R80
163:R40
160:R20
157:R10
118:butt
96:(18
3497:-20
3492:-17
3487:-14
3482:-12
3477:-11
3472:-10
3158:-28
3153:-22
3148:-21
3143:-11
2935:-16
2930:-15
2925:-14
2920:-13
2915:-12
2910:-11
2905:-10
2321:999
2316:965
2311:898
2306:860
2301:843
2296:838
2291:764
2286:732
2281:704
2276:690
2271:668
2266:657
2261:646
2229:639
2224:519
2219:518
2214:500
2209:361
2204:306
2199:302
2194:262
2189:261
2184:259
2179:233
2174:228
2169:226
2164:217
2159:216
2154:128
2142:-13
2137:-12
2132:-11
2127:-10
1996:ISO
1887:doi
1844:doi
1809:doi
1362:or
1337:10
1334:10
1331:10
1288:7.0
1273:6.0
1268:6.0
1263:6.0
1248:5.5
1185:3.5
1170:3.0
1165:3.0
1073:1.5
1068:1.5
1040:1.2
1035:1.2
154:R5
122:tun
88:If
32:ISO
4300::
3798:-2
3793:-1
3626:-2
3584:-9
3579:-3
3467:-6
3462:-3
3457:-2
3350:-2
3345:-1
3289:-2
2900:-9
2890:-8
2885:-7
2880:-6
2875:-5
2870:-4
2865:-3
2860:-2
2855:-1
2718:-1
2496:-3
2491:-2
2486:-1
2254:-6
2249:-5
2244:-3
2239:-2
2234:-1
2122:-9
2117:-8
2112:-7
2107:-6
2102:-5
2097:-4
2092:-3
2087:-1
2082:-0
2077:31
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2016:–
2012:–
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1945:43
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2062:9
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2032:1
1988:e
1981:t
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1383:n
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