1、Designation: E29 13 (Reapproved 2019) An American National StandardStandard Practice forUsing Significant Digits in Test Data to DetermineConformance with Specifications1This standard is issued under the fixed designation E29; the number immediately following the designation indicates the year of or
2、iginaladoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.Asuperscriptepsilon () indicates an editorial change since the last revision or reapproval.This standard has been approved for use by agencies of the U.S. Department of
3、Defense.1. Scope1.1 This practice is intended to assist the various technicalcommittees in the use of uniform methods of indicating thenumber of digits which are to be considered significant inspecification limits, for example, specified maximum valuesand specified minimum values. Its aim is to outl
4、ine methodswhich should aid in clarifying the intended meaning ofspecification limits with which observed values or calculatedtest results are compared in determining conformance withspecifications.1.2 This practice is intended to be used in determiningconformance with specifications when the applic
5、able ASTMspecifications or standards make direct reference to this prac-tice.1.3 Reference to this practice is valid only when a choice ofmethod has been indicated, that is, either absolute method orrounding method.1.4 The system of units for this practice is not speci-fied. Dimensional quantities i
6、n the practice are presented onlyas illustrations of calculation methods. The examples are notbinding on products or test methods treated.1.5 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to
7、establish appro-priate safety, health, and environmental practices and deter-mine the applicability of regulatory limitations prior to use.1.6 This international standard was developed in accor-dance with internationally recognized principles on standard-ization established in the Decision on Princi
8、ples for theDevelopment of International Standards, Guides and Recom-mendations issued by the World Trade Organization TechnicalBarriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:2E177 Practice for Use of the Terms Precision and Bias inASTM Test MethodsE456 Terminology Relat
9、ing to Quality and StatisticsE2282 Guide for Defining the Test Result of a Test MethodIEEE/ASTM SI 10 Standard for Use of the InternationalSystem of Units (SI): The Modern Metric System3. Terminology3.1 DefinitionsTerminology E456 provides a more exten-sive list of terms in E11 standards.3.1.1 obser
10、ved value, nthe value obtained by making anobservation. E22823.1.2 repeatability conditions, nconditions where inde-pendent test results are obtained with the same method onidentical test items in the same laboratory by the same operatorusing the same equipment within short intervals of time. E1773.
11、1.3 repeatability standard deviation (sr), nthe standarddeviation of test results obtained under repeatabilityconditions. E1773.1.4 significant digitany of the figures 0 through 9 that isused with its place value to denote a numerical quantity tosome desired approximation, excepting all leading zero
12、s andsome trailing zeros in numbers not represented with a decimalpoint.3.1.4.1 DiscussionThis definition of significant digits re-lates to how the number is represented as a decimal. It shouldnot be inferred that a measurement value is precise to thenumber of significant digits used to represent it
13、.3.1.4.2 DiscussionThe digit zero may either indicate aspecific value or indicate place only. Zeros leading the firstnonzero digit of a number indicate order of magnitude only andare not significant digits. For example, the number 0.0034 hastwo significant digits. Zeros trailing the last nonzero dig
14、it for1This practice is under the jurisdiction ofASTM Committee E11 on Quality andStatistics and is the direct responsibility of Subcommittee E11.30 on StatisticalQuality Control.Current edition approved Jan. 1, 2019. Published January 2019. Originallyapproved in 1940. Last previous edition approved
15、 in 2013 as E29 13. DOI:10.1520/E0029-13R19.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.Copyright ASTM In
16、ternational, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United StatesThis international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standard
17、s, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.1numbers represented with a decimal point are significant digits.For example, the numbers 1270. and 32.00 each have foursignificant digits.The significance of trailing zeros for numbersre
18、presented without use of a decimal point can only beidentified from knowledge of the source of the value. Forexample, a modulus strength, stated as 140 000 Pa, may haveas few as two or as many as six significant digits.3.1.4.3 DiscussionTo eliminate ambiguity, the exponen-tial notation may be used.
19、Thus, 1.40 105indicates that themodulus is reported to the nearest 0.01 105or 1000 Pa.3.1.4.4 DiscussionUse of appropriate SI prefixes is rec-ommended for metric units to reduce the need for trailing zerosof uncertain significance. Thus, 140 kPa (without the decimalpoint) indicates that the modulus
20、is reported either to thenearest 10 or 1 kPa, which is ambiguous with respect to thenumber of significant digits. However, 0.140 MPa clearlyindicates that the modulus is reported to the nearest 1 kPa, and0.14 MPa clearly indicates that the modulus is reported to thenearest 10 kPa.3.1.5 test result,
21、nthe value of a characteristic obtained bycarrying out a specified test method. E22824. Significance and Use4.1 This practice describes two commonly accepted meth-ods of rounding data, identified as theAbsolute Method and theRounding Method. In the applications of this practice to aspecific material
22、 or materials it is essential to specify whichmethod is intended to apply. In the absence of suchspecification, reference to this practice, which expresses nopreference as to which method should apply, would be mean-ingless. The choice of method depends upon the currentpractice of the particular bra
23、nch of industry or technologyconcerned, and should therefore be specified in the primepublication.4.1.1 The unqualified statement of a numerical limit, such as“2.50 in. max,” cannot, in view of different establishedpractices and customs, be regarded as carrying a definiteoperational meaning concerni
24、ng the number of digits to beretained in an observed or a calculated value for purposes ofdetermining conformance with specifications.4.1.2 Absolute MethodIn some fields, specification limitsof 2.5 in. max, 2.50 in. max, and 2.500 in. max are all taken toimply the same absolute limit of exactly two
25、and a half inchesand for purposes of determining conformance withspecifications, an observed value or a calculated value is to becompared directly with the specified limit. Thus, any deviation,however small, outside the specification limit signifies noncon-formance with the specifications. This will
26、 be referred to as theabsolute method, which is discussed in Section 5.4.1.3 Rounding MethodIn other fields, specification limitsof 2.5 in. max, 2.50 in. max, 2.500 in. max are taken to implythat, for the purposes of determining conformance withspecifications, an observed value or a calculated value
27、 shouldbe rounded to the nearest 0.1 in., 0.01 in., 0.001 in.,respectively, and then compared with the specification limit.This will be referred to as the rounding method, which isdiscussed in Section 6.4.2 Section 7 of this practice gives guidelines for use inrecording, calculating, and reporting t
28、he final result for testdata.5. Absolute Method5.1 Where ApplicableThe absolute method applies whereit is the intent that all digits in an observed value or a calculatedvalue are to be considered significant for purposes of deter-mining conformance with specifications. Under theseconditions, the spe
29、cified limits are referred to as absolutelimits.5.2 How AppliedWith the absolute method, an observedvalue or a calculated value is not to be rounded, but is to becompared directly with the specified limiting value. Confor-mance or nonconformance with the specification is based onthis comparison.5.3
30、How ExpressedThis intent may be expressed in thestandard in one of the following forms:5.3.1 If the absolute method is to apply to all specified limitsin the standard, this may be indicated by including thefollowing sentence in the standard:For purposes of determining conformance with these specific
31、ations, allspecified limits in this standard are absolute limits, as defined in ASTM PracticeE29, for Using Significant Digits in Test Data to Determine Conformance withSpecifications.5.3.2 If the absolute method is to apply to all specified limitsof some general type in the standard (such as dimens
32、ionaltolerance limits), this may be indicated by including thefollowing sentence in the standard:For purposes of determining conformance with these specifications, allspecified (dimensional tolerance) limits are absolute limits, as defined in ASTMPractice E29, for Using Significant Digits in Test Da
33、ta to Determine Confor-mance with Specifications.5.3.3 If the absolute method is to apply to all specified limitsgiven in a table, this may be indicated by including a footnotewith the table as follows:CapacitymLVolumetric ToleranceAmL10 0.0225 0.0350 0.05100 0.10ATolerance limits specified are abso
34、lute limits as defined in Practice E29, for UsingSignificant Digits in Test Data to Determine Conformance with Specifications.6. Rounding Method6.1 Where ApplicableThe rounding method applies whereit is the intent that a limited number of digits in an observedvalue or a calculated value are to be co
35、nsidered significant forpurposes of determining conformance with specifications.6.2 How AppliedWith the rounding method, an observedvalue or a calculated value should be rounded by the procedureprescribed in 4.1.3 to the nearest unit in the designated place offigures stated in the standard, as, for
36、example, “to the nearestkPa,” “to the nearest 10 ohms,” “to the nearest 0.1 percent,”etc. The rounded value should then be compared with thespecified limit, and conformance or nonconformance with thespecification based on this comparison.E29 13 (2019)26.3 How ExpressedThis intent may be expressed in
37、 thestandard in one of the following forms:6.3.1 If the rounding method is to apply to all specifiedlimits in the standard, and if all digits expressed in thespecification limit are to be considered significant, this may beindicated by including the following statement in the standard:The following
38、applies to all specified limits in this standard: For purposes ofdetermining conformance with these specifications, an observed value or acalculated value shall be rounded “to the nearest unit” in the last right-hand digitused in expressing the specification limit, in accordance with the roundingmet
39、hod 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 specifiedlimits for certain selected requirements, this may be indicatedby including the following statement in the standard:The foll
40、owing applies to specified limits for requirements on (tensilestrength), (elongation), and ( . ) given in ., (applicable section number andtitle) and ( . ) of this standard: For purposes of determining conformance withthese specifications, an observed value or a calculated value shall be roundedto t
41、he nearest 1 kPa for (tensile strength), to the nearest (1 percent) for(elongation), and to the nearest ( . ) for ( . ) in accordance with the roundingmethod of ASTM Practice E29 Using Significant Digits in Test Data to Deter-mine Conformance with Specifications.6.3.3 If the rounding method is to ap
42、ply to all specifiedlimits in a table, this may be indicated by a note in the mannershown in the following examples:6.3.3.1 Example 1Same significant digits for all items:Chemical Composition,% massCopper 4.5 0.5Iron 1.0 maxSilicon 2.5 0.5Other constituents (magnesium + zinc + manganese) 0.5 maxAlum
43、inum remainderFor purposes of determining conformance with these specifications, anobserved value or a calculated value shall be rounded to the nearest 0.1percent, in accordance with the rounding method of ASTM Practice E29 UsingSignificant Digits in Test Data to Determine Conformance with Specifica
44、tions.6.3.3.2 Example 2Significant digits not the same for allitems; similar requirements:Chemical Composition, % massmin maxNickel 57 .Chromium 14 18Manganese . 3Silicon . 0.40Carbon . 0.25Sulfur . 0.03Iron remainderFor purposes of determining conformance with these specifications, anobserved value
45、 or a calculated value shall be rounded “to the nearest unit” inthe last right-hand significant digit used in expressing the limiting value, inaccordance with the rounding method of ASTM Practice E29 Using SignificantDigits in Test Data to Determine Conformance with Specifications.6.3.3.3 Example 3S
46、ignificant digits not the same for allitems; dissimilar requirements:Tensile RequirementsTensile strength, psi 60 000 to 72 000Yield point, min, psi 33 000Elongation in 2 in., min % 22For purposes of determination of conformance with these specifications, anobserved value or a calculated value shall
47、 be rounded to the nearest 1000 psifor tensile strength and yield point and to the nearest 1 percent for elongation,in accordance with the rounding method of ASTM Practice E29 Using Signifi-cant Digits in Test Data to Determine Conformance with Specifications.6.4 Rounding ProcedureThe actual roundin
48、g procedure3shall be as follows:6.4.1 When the digit next beyond the last place to beretained is less than 5, retain unchanged the digit in the lastplace retained.6.4.2 When the digit next beyond the last place to beretained is greater than 5, increase by 1 the digit in the lastplace retained.6.4.3
49、When the digit next beyond the last place to beretained is 5, and there are no digits beyond this 5, or onlyzeros, increase by 1 the digit in the last place retained if it isodd, leave the digit unchanged if it is even. Increase by 1 thedigit in the last place retained, if there are non-zero digitsbeyond this 5.NOTE 1This method for rounding 5s is not universally used bysoftware packages.6.4.4 This rounding procedure may be restated simply asfollows: When rounding a number to one having a specifiednumber of significant digits, choose that which is ne
