1、Designation: E29 08E29 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 originaladopti
2、on 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 Department of Defense.1. Scope*
3、1.1 This practice is intended to assist the various technical committees in the use of uniform methods of indicating the numberof digits which are to be considered significant in specification limits, for example, specified maximum values and specifiedminimum values. Its aim is to outline methods wh
4、ich should aid in clarifying the intended meaning of specification limits withwhich observed values or calculated test results are compared in determining conformance with specifications.1.2 This practice is intended to be used in determining conformance with specifications when the applicable ASTMs
5、pecifications or standards make direct reference to this practice.1.3 Reference to this practice is valid only when a choice of method has been indicated, that is, either absolute method orrounding method.1.4 The system of units for this practice is not specified. Dimensional quantities in the pract
6、ice are presented only as illustrationsof 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 the responsibilityof the user of this standard to establish
7、 appropriate safety and health practices and determine the applicability of regulatorylimitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E177 Practice for Use of the Terms Precision and Bias in ASTM Test MethodsE456 Terminology Relating to Quality and StatisticsE2282 Guide for Defin
8、ing the Test Result of a Test MethodIEEE/ASTM SI 10 Standard for Use of the International System of Units (SI): The Modern Metric System3. Terminology3.1 Definitions:DefinitionsTerminologyTerminology E456 provides a more extensive list of terms in E11 standards.3.1.1 observed value, nthe value obtai
9、ned by making an observation. E22823.1.2 repeatability conditions, nconditions where independent test results are obtained with the same method on identical testitems in the same laboratory by the same operator using the same equipment within short intervals of time. E1773.1.3 repeatability standard
10、 deviation (sr), nthe standard deviation of test results obtained under repeatability conditions.E1773.1.4 significant digitany of the figures 0 through 9 that is used with its place value to denote a numerical quantity to somedesired approximation, excepting all leading zeros and some trailing zero
11、s in numbers not represented with a decimal point.3.1.4.1 Discussion1 This practice is under the jurisdiction of ASTM Committee E11 on Quality and Statistics and is the direct responsibility of Subcommittee E11.30 on Statistical QualityControl.Current edition approved Oct. 1, 2008Aug. 1, 2013. Publi
12、shed October 2008August 2013. Originally approved in 1940. Last previous edition approved in 20062008 asE29 06b.E29 08. DOI: 10.1520/E0029-08.10.1520/E0029-13.2 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at serviceastm.org. For Annual Book of A
13、STM Standardsvolume information, refer to the standards Document Summary page on the ASTM website.This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Becauseit may not be technically
14、possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current versionof the standard as published by ASTM is to be considered the official document.*A Summary of Changes section appears at the end of this standar
15、dCopyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1This definition of significant digits relates to how the number is represented as a decimal. It should not be inferred that ameasurement value is precise to the number of significant di
16、gits used to represent it.3.1.4.2 DiscussionThe digit zero may either indicate a specific value or indicate place only. Zeros leading the first nonzero digit of a number indicateorder of magnitude only and are not significant digits. For example, the number 0.0034 has two significant digits. Zeros t
17、railingthe last nonzero digit for numbers represented with a decimal point are significant digits. For example, the numbers 1270. and32.00 each have four significant digits. The significance of trailing zeros for numbers represented without use of a decimal pointcan only be identified from knowledge
18、 of the source of the value. For example, 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 exponential notation may be used.Thus, 1.40 105 indicates that the modulus is reported to the nearest0.01 105 o
19、r 1000 Pa.3.1.4.4 DiscussionUse of appropriate SI prefixes is recommended for metric units to reduce the need for trailing zeros of uncertain significance. Thus,140 kPa (without the decimal point) indicates that the modulus is reported either to the nearest 10 or 1 kPa, which is ambiguouswith respec
20、t to the number of significant digits. However, 0.140 MPa clearly indicates that the modulus is reported to the nearest1 kPa, and 0.14 MPa clearly indicates that the modulus is reported to the nearest 10 kPa.3.1.5 test result, nthe value of a characteristic obtained by carrying out a specified test
21、method. E22824. Significance and Use4.1 This practice describes two commonly accepted methods of rounding data, identified as the Absolute Method and theRounding Method. In the applications of this practice to a specific material or materials it is essential to specify which method isintended to app
22、ly. In the absence of such specification, reference to this practice, which expresses no preference as to which methodshould apply, would be meaningless. The choice of method depends upon the current practice of the particular branch of industryor technology concerned, and should therefore be specif
23、ied in the prime publication.4.1.1 The unqualified statement of a numerical limit, such as “2.50 in. max,” cannot, in view of different established practicesand customs, be regarded as carrying a definite operational meaning concerning the number of digits to be retained in an observedor a calculate
24、d value for purposes of determining conformance with specifications.4.1.2 Absolute MethodIn some fields, specification limits of 2.5 in. max, 2.50 in. max, and 2.500 in. max are all taken to implythe same absolute limit of exactly two and a half inches and for purposes of determining conformance wit
25、h specifications, anobserved value or a calculated value is to be compared directly with the specified limit.Thus, any deviation, however small, outsidethe specification limit signifies nonconformance with the specifications. This will be referred to as the absolute method, which isdiscussed in Sect
26、ion 5.4.1.3 Rounding MethodIn other fields, specification limits of 2.5 in. max, 2.50 in. max, 2.500 in. max are taken to imply that,for the purposes of determining conformance with specifications, an observed value or a calculated value should be rounded to thenearest 0.1 in., 0.01 in., 0.001 in.,
27、respectively, and then compared with the specification limit. This will be referred to as therounding method,which is discussed in Section 6.4.2 Section 7 of this practice gives guidelines for use in recording, calculating, and reporting the final result for test data.5. Absolute Method5.1 Where App
28、licableThe absolute method applies where it is the intent that all digits in an observed value or a calculatedvalue are to be considered significant for purposes of determining conformance with specifications. Under these conditions, thespecified limits are referred to as absolute limits.5.2 How App
29、liedWith the absolute method, an observed value or a calculated value is not to be rounded, but is to be compareddirectly with the specified limiting value. Conformance or nonconformance with the specification is based on this comparison.5.3 How ExpressedThis intent may be expressed in the standard
30、in one of the following forms:5.3.1 If the absolute method is to apply to all specified limits in the standard, this may be indicated by including the followingsentence in the standard:E29 132For purposes of determining conformance with these specification, allspecified limits in this standard are a
31、bsolute 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 limits of some general type in the standard (such as dimensional tolerancelimits), this may be indicated by
32、including the following 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 Confor-mance with Specifications
33、.5.3.3 If the absolute method is to apply to all specified limits given in a table, this may be indicated by including a footnotewith the table as follows:CapacitymLVolumetric ToleranceA mL10 0.0225 0.0350 0.05100 0.10A Tolerance limits specified are absolute limits as defined in Practice E29, for U
34、sing Significant Digits in Test Data to Determine Conformance with Specifications.6. Rounding Method6.1 Where ApplicableThe rounding method applies where it is the intent that a limited number of digits in an observed valueor a calculated value are to be considered significant for purposes of determ
35、ining conformance with specifications.6.2 How AppliedWith the rounding method, an observed value or a calculated value should be rounded by the procedureprescribed in 4.1.3 to the nearest unit in the designated place of figures stated in the standard, as, for example, “to the nearest kPa,”“to the ne
36、arest 10 ohms,” “to the nearest 0.1 percent,” etc. The rounded value should then be compared with the specified limit,and conformance or nonconformance with the specification based on this comparison.6.3 How ExpressedThis intent may be expressed in the standard in one of the following forms:6.3.1 If
37、 the rounding method is to apply to all specified limits in the standard, and if all digits expressed in the specification limitare to be considered significant, this may be indicated by including the following statement in the standard:The following applies to all specified limits in this standard:
38、 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, for Using Significant D
39、igits in Test Data to Deter-mine Conformance with Specifications.6.3.2 If the rounding method is to apply only to the specified limits for certain selected requirements, this may be indicated byincluding the following statement in the standard:The following applies to specified limits for requiremen
40、ts 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 (tensile strength), to the n
41、earest (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 specified limits in a table, this may
42、be indicated by a note in the manner shownin 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 of determining confor
43、mance 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 2Significant digits not th
44、e same for all items; similar requirements:Chemical Composition, % massE29 133min 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 be rounded
45、“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 same for all i
46、tems; 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 1000 psifor
47、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 procedure3 shall be as follows:6.4.1
48、When the digit next beyond 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 place retained.6.4.3 When the digit next beyond the las
49、t place to be retained is 5, and there are no digits beyond this 5, or only zeros, increaseby 1 the digit in the last place retained if it is odd, leave the digit unchanged if it is even. Increase by 1 the digit in the last placeretained, if there are non-zero digits beyond this 5.NOTE 1This method for rounding 5s is not universally used by software packages.6.4.4 This rounding procedure may be restated simply as follows: When rounding a number to one having a specified numberof significant digits, choose that which is nearest. If two choices a
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