1、Designation: E29 13 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 originaladoption or,
2、 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 Department of Defense.1. Scope*1.1 Th
3、is 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 outline methodswhich shoul
4、d 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 applicable ASTMspecification
5、s 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 in the practice are pre
6、sented 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 establish appro-priate
7、 safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E177 Practice for Use of the Terms Precision and Bias inASTM Test MethodsE456 Terminology Relating to Quality and StatisticsE2282 Guide for Defining the Tes
8、t 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 observed value, nthe value obtained by making anobservation. E2282
9、3.1.2 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. E1773.1.3 repeatability standard deviation (sr), nthe standarddevia
10、tion 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 zeros andsome trailing zeros in numbers not represented with a de
11、cimalpoint.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.3.1.4.2 DiscussionThe digit zero may either indicate aspecif
12、ic 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 digit fornumbers represented with a decimal point are significan
13、t digits.For example, the numbers 1270. and 32.00 each have foursignificant digits.The significance of trailing zeros for numbersrepresented 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 havea
14、s few as two or as many as six significant digits.1This 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 Aug. 1, 2013. Published August 2013. Originallyappro
15、ved in 1940. Last previous edition approved in 2008 as E29 08. DOI:10.1520/E0029-13.2For 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 p
16、age onthe ASTM website.*A Summary 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 States13.1.4.3 DiscussionTo eliminate ambiguity, the exponen-tial notation may be used. Thus, 1.40 105ind
17、icates 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 is reported eithe
18、r 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, nthe value of a c
19、haracteristic 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 or materials it
20、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 branch of industry o
21、r 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 concerning the number of
22、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 and a half inches
23、and 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 be referred to a
24、s 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 shouldbe rounded
25、 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 the final result fo
26、r 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 specified limits are
27、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 How ExpressedThis
28、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 specification, allspecifie
29、d 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 dimensionaltolerance limi
30、ts), 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 Data to Determine Con
31、for-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 absolute limits as defi
32、ned 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 considered significan
33、t 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 example, “to the ne
34、arestkPa,” “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.6.3 How ExpressedThis intent may be expressed in thestandard in one of the follow
35、ing 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:E29132The following applies to all specified li
36、mits 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 roundingmethod of ASTM Practice E29, f
37、or 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 following applies to specified
38、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 the nearest 1kPa for (tensil
39、e 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 apply to all specifiedlimits i
40、n 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 maxAluminum remainderFor purposes o
41、f 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 Specifications.6.3.3.2 Example 2Signi
42、ficant 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 or a calculated value shall
43、 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 3Significant digits not the sa
44、me 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 be rounded to the nearest 1
45、000 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 rounding procedure3shall be as foll
46、ows: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 When the digit next beyond t
47、he 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 meth
48、od 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 nearest. Iftwo choices are possible, as when the digits dropped areexactly
49、a5ora5followed only by zeros, choose that endingin an even digit. Table 1 gives examples of applying thisrounding procedure.6.5 The rounded value should be obtained in one step bydirect rounding of the most precise value available and not intwo or more successive roundings. For example: 89 490rounded to the nearest 1 000 is at once 89 000; it would beincorrect to round first to the nearest 100, giving 89 500 andthen to the 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
