astm-e29-2013

1、Designation: E29 ? 13 An American National StandardStandard Practice for Using Significant Digits in Test Data to Determine Conformance with Specifications1This standard is issued under the fixed designation E29; the num

2、ber immediately following the designation indicates the year of original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A superscript epsil

3、on (´) indicates an editorial change since the last revision or reapproval.This standard has been approved for use by agencies of the Department of Defense.1. Scope*1.1 This practice is intended to assist the variou

4、s technical committees in the use of uniform methods of indicating the number of digits which are to be considered significant in specification limits, for example, specified maximum values and specified minimum values.

5、Its aim is to outline methods which should aid in clarifying the intended meaning of specification limits with which observed values or calculated test results are compared in determining conformance with specifications.

6、1.2 This practice is intended to be used in determining conformance with specifications when the applicable ASTM specifications or standards make direct reference to this prac- tice.1.3 Reference to this practice is vali

7、d only when a choice of method has been indicated, that is, either absolute method or rounding method.1.4 The system of units for this practice is not speci- fied. Dimensional quantities in the practice are presented onl

8、y as illustrations of calculation methods. The examples are not binding on products or test methods treated.1.5 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is

9、 the responsibility of the user of this standard to establish appro- priate safety and health practices and determine the applica- bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2

10、E177 Practice for Use of the Terms Precision and Bias inASTM Test MethodsE456 Terminology Relating to Quality and Statistics E2282 Guide for Defining the Test Result of a Test Method IEEE/ASTM SI 10 Standard for Use of t

11、he International System of Units (SI): The Modern Metric System3. Terminology3.1 Definitions—Terminology E456 provides a more exten- sive list of terms in E11 standards.3.1.1 observed value, n—the value obtained by makin

12、g an observation. E22823.1.2 repeatability conditions, n—conditions where inde- pendent test results are obtained with the same method on identical test items in the same laboratory by the same operator using the same eq

13、uipment within short intervals of time. E1773.1.3 repeatability standard deviation (sr), n—the standard deviation of test results obtained under repeatability conditions. E1773.1.4 significant digit—any of the figures 0

14、through 9 that is used with its place value to denote a numerical quantity to some desired approximation, excepting all leading zeros and some trailing zeros in numbers not represented with a decimal point.3.1.4.1 Discus

15、sion—This definition of significant digits re- lates to how the number is represented as a decimal. It should not be inferred that a measurement value is precise to the number of significant digits used to represent it.3

16、.1.4.2 Discussion—The digit zero may either indicate a specific value or indicate place only. Zeros leading the first nonzero digit of a number indicate order of magnitude only and are not significant digits. For example

17、, the number 0.0034 has two significant digits. Zeros trailing the last nonzero digit for numbers represented with a decimal point are significant digits. For example, the numbers 1270. and 32.00 each have four significa

18、nt digits. The significance of trailing zeros for numbers represented without use of a decimal point can only be identified from knowledge of the source of the value. For example, a modulus strength, stated as 140 000 Pa

19、, may have as few as two or as many as six significant digits.1 This practice is under the jurisdiction of ASTM Committee E11 on Quality and Statistics and is the direct responsibility of Subcommittee E11.30 on Statistic

20、al Quality Control. Current edition approved Aug. 1, 2013. Published August 2013. Originally approved in 1940. Last previous edition approved in 2008 as E29 – 08. DOI: 10.1520/E0029-13. 2 For referenced ASTM standards, v

21、isit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards volume information, refer to the standard’s Document Summary page on the ASTM website.*A Summar

22、y of Changes section appears at the end of this standardCopyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1 Copyright ASTM International Provided by

23、IHS under license with ASTM Not for Resale No reproduction or networking permitted without license from IHS--`,,```,,,,````-`-`,,`,,`,`,,`---The following applies to all specified limits in this standard: For purposes of

24、 determining conformance with these specifications, an observed value or a calculated value shall be rounded “to the nearest unit” in the last right-hand digit used in expressing the specification limit, in accordance wi

25、th the rounding method of ASTM Practice E29, for Using Significant Digits in Test Data to De- termine Conformance with Specifications.6.3.2 If the rounding method is to apply only to the specified limits for certain sele

26、cted requirements, this may be indicated by including the following statement in the standard:The following applies to specified limits for requirements on (tensile strength), (elongation), and ( ... ) given in ..., (app

27、licable section number and title) and ( ... ) of this standard: For purposes of determining conformance with these specifications, an observed value or a calculated value shall be rounded to the nearest 1kPa for (tensile

28、 strength), to the nearest (1 percent) for (elongation), and to the nearest ( ... ) for ( ... ) in accordance with the rounding method of ASTM Practice E29 Using Significant Digits in Test Data to Deter- mine Conformance

29、 with Specifications.6.3.3 If the rounding method is to apply to all specified limits in a table, this may be indicated by a note in the manner shown in the following examples: 6.3.3.1 Example 1—Same significant digits f

30、or all items:Chemical Composition, % massCopper 4.5 ± 0.5 Iron 1.0 max Silicon 2.5 ± 0.5 Other constituents (magnesium + zinc + manganese) 0.5 max Aluminum remainderFor purposes of determining conformance with

31、these specifications, an observed value or a calculated value shall be rounded to the nearest 0.1 percent, in accordance with the rounding method of ASTM Practice E29 Using Significant Digits in Test Data to Determine Co

32、nformance with Specifications.6.3.3.2 Example 2—Significant digits not the same for all items; similar requirements:Chemical Composition, % mass min maxNickel 57 ... Chromium 14 18 Manganese ... 3 Silicon ... 0.40 Carbon

33、 ... 0.25 Sulfur ... 0.03 Iron remainderFor purposes of determining conformance with these specifications, an observed value or a calculated value shall be rounded “to the nearest unit” in the last right-hand significant

34、 digit used in expressing the limiting value, in accordance with the rounding method of ASTM Practice E29 Using Significant Digits in Test Data to Determine Conformance with Specifications.6.3.3.3 Example 3—Significant d

35、igits not the same for all items; dissimilar requirements:Tensile RequirementsTensile strength, psi 60 000 to 72 000 Yield point, min, psi 33 000 Elongation in 2 in., min % 22For purposes of determination of conformance

36、with these specifications, an observed value or a calculated value shall be rounded to the nearest 1000 psi for tensile strength and yield point and to the nearest 1 percent for elongation, in accordance with the roundin

37、g method of ASTM Practice E29 Using Signifi- cant Digits in Test Data to Determine Conformance with Specifications.6.4 Rounding Procedure—The actual rounding procedure3shall be as follows:6.4.1 When the digit next beyond

38、 the last place to be retained is less than 5, retain unchanged the digit in the last place retained. 6.4.2 When the digit next beyond the last place to be retained is greater than 5, increase by 1 the digit in the last

39、place retained. 6.4.3 When the digit next beyond the last place to be retained is 5, and there are no digits beyond this 5, or only zeros, increase by 1 the digit in the last place retained if it is odd, leave the digit

40、unchanged if it is even. Increase by 1 the digit in the last place retained, if there are non-zero digits beyond this 5.NOTE 1—This method for rounding 5’s is not universally used by software packages.6.4.4 This rounding

41、 procedure may be restated simply as follows: When rounding a number to one having a specified number of significant digits, choose that which is nearest. If two choices are possible, as when the digits dropped are exact

42、ly a 5 or a 5 followed only by zeros, choose that ending in an even digit. Table 1 gives examples of applying this rounding procedure.6.5 The rounded value should be obtained in one step by direct rounding of the most pr

43、ecise value available and not in two or more successive roundings. For example: 89 490 rounded to the nearest 1 000 is at once 89 000; it would be incorrect to round first to the nearest 100, giving 89 500 and then to th

44、e nearest 1 000, giving 90 000.6.6 Special Case, Rounding to the Nearest 50, 5, 0.5, 0.05, etc.—If in special cases it is desired to specify rounding to the nearest 50, 5, 0.5, 0.05, etc., this may be done by so indicati

45、ng in the standard. In order to round to the nearest 50, 5, 0.5, 0.05, etc., double the observed or calculated value, round to the nearest 100, 10, 1.0, 0.10, etc., in accordance with the procedure in 6.4, and divide by

46、2. For example, in rounding 6 025 to the nearest 50, 6 025 is doubled giving 12 050 which becomes 12 000 when rounded to the nearest 100 (6.4.3). When 12 000 is divided by 2, the resulting number, 6 000, is the rounded v

47、alue of 6 025. In rounding 6 075 to the nearest 50,3 The rounding procedure given in this practice is the same as the one given in the ASTM Manual 7 on Presentation of Data and Control Chart Analysis.TABLE 1 ExamplesA of

48、 RoundingSpecified LimitObserved Value or Calculated ValueTo Be Rounded to NearestRounded Value to be Used for Purposes of Determining ConformanceConforms with Specified LimitYield point, 36 000 psi, min 35 940h 35 950 3

49、5 960100 psi 100 psi 100 psi35 900 36 000 36 000no yes yesNickel, 57 %, mass, min 56.4h 56.5 56.61 % 1 % 1 %56 56 57no no yesWater extract conductivity, 40 ms/m, max40.4h 40.5 40.61 ms/m 1 ms/m 1 ms/m40 40 41yes yes noSo

50、dium bicarbonate 0.5 %, max, dry mass basis0.54h 0.55 0.560.1 % 0.1 % 0.1 %0.5 0.6 0.6yes no noA These examples are meant to illustrate rounding rules and do not necessarily reflect the usual number of digits associated