1、Designation: E 29 06bAn American National StandardStandard Practice forUsing Significant Digits in Test Data to DetermineConformance with Specifications1This standard is issued under the fixed designation E 29; the number immediately following the designation indicates the year of originaladoption o
2、r, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A superscriptepsilon (e) 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 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 methodswhic
4、h 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 applicable ASTMspecif
5、ications 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.2. Referenced Documents2.1 ASTM Standards:2E 456 Terminology Relating to Quality and StatisticsE 228
6、2 Guide for Defining the Test Result of a Test MethodSI 10 Standard for Use of the International System of Units(SI) (the Modernized Metric System)3. Terminology3.1 Definitions:3.2 observed value, nthe value obtained by making anobservation. E 22823.3 significant digitany of the figures 0 through 9,
7、 except-ing all leading zeros and some trailing zeros in numbers notrepresented with a decimal point, which is used with its placevalue to denote a numerical quantity to some desired approxi-mation.NOTE 1The digit zero may either indicate a specific value or indicateplace only. Zeros leading the fir
8、st nonzero digit of a number indicate orderof magnitude only and are not significant digits. For example, the number0.0034 has two significant digits. Zeros trailing the last nonzero digit fornumbers represented with a decimal point are significant digits. Forexample, the numbers 1270. and 32.00 eac
9、h have four significant digits.The significance of trailing zeros for numbers represented without use ofa decimal point can only be identified from knowledge of the source of thevalue. For example, a modulus strength, stated as 140 000 Pa, may haveas few as two or as many as six significant digits.N
10、OTE 2To eliminate ambiguity, the exponential notation may beused. Thus, 1.40 3 105indicates that the modulus is reported to thenearest 0.01 3 105or 1000 Pa.NOTE 3Use of appropriate SI prefixes is recommended for metricunits to reduce the need for trailing zeros of uncertain significance. Thus,140 kP
11、a (without the decimal point) indicates that the modulus is reportedeither to the nearest 10 or 1 kPa, which is ambiguous with respect to thenumber of significant digits. However, 0.140 MPa clearly indicates thatthe modulus is reported to the nearest 1 kPa, and 0.14 MPa clearlyindicates that the mod
12、ulus is reported to the nearest 10 kPa.3.4 test result, nthe value of a characteristic obtained bycarrying out a specified test method. E 22824. Significance and Use4.1 This practice describes two commonly accepted meth-ods of rounding data, identified as theAbsolute Method and theRounding Method. I
13、n the applications of this practice to aspecific material or materials it is essential to specify whichmethod is intended to apply. In the absence of such specifica-tion, reference to this practice, which expresses no preferenceas to which method should apply, would be meaningless. Thechoice of meth
14、od depends upon the current practice of theparticular branch of industry or technology concerned, andshould therefore be specified 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 establishedpractices and customs, be r
15、egarded as carrying a definiteoperational meaning concerning 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
16、 all taken toimply the same absolute limit of exactly two and a half inches1This practice is under the jurisdiction of ASTM Committee E11 on Quality andStatistics and is the direct responsibility of Subcommittee E11.30 on Data Analysis.Current edition approved Nov. 15, 2006. Published December 2006.
17、 Originallyapproved in 1940. Last previous edition approved in 2006 as E 29 06a.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
18、onthe ASTM website.1*A Summary of Changes section appears at the end of this standard.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.and for purposes of determining conformance with specifica-tions, an observed value or a calculated
19、value is to be compareddirectly with the specified limit. Thus, any deviation, howeversmall, outside the specification limit signifies nonconformancewith the specifications. This will be referred to as the absolutemethod, which is discussed in 5.4.1.3 Rounding MethodIn other fields, specification li
20、mitsof 2.5 in. max, 2.50 in. max, 2.500 in. max are taken to implythat, for the purposes of determining conformance with speci-fications, an observed value or a calculated value should berounded to the nearest 0.1 in., 0.01 in., 0.001 in., respectively,and then compared with the specification limit.
21、 This will bereferred to as the rounding method,which is discussed in 6.4.2 Section 7 of this practice gives guidelines for use inrecording, calculating, and reporting the final result for testdata.5. Absolute Method5.1 Where ApplicableThe absolute method applies whereit is the intent that all digit
22、s in an observed value or a calculatedvalue are to be considered significant for purposes of deter-mining conformance with specifications. Under these condi-tions, the specified limits are referred to as absolute limits.5.2 How AppliedWith the absolute method, an observedvalue or a calculated value
23、is not to be rounded, but is to becompared directly with the specified limiting value. Conform-ance or nonconformance with the specification is based on thiscomparison.5.3 How ExpressedThis intent may be expressed in thestandard in one of the following forms:5.3.1 If the absolute method is to apply
24、to all specified limitsin the standard, this may be indicated by including thefollowing sentence in the standard:For purposes of determining conformance with these speci-fications, all specified limits in this standard are absolute limits,as defined in ASTM Practice E 29, for Using Significant Digit
25、sin Test Data to Determine Conformance with Specifications.5.3.2 If the absolute method is to apply to all specified limitsof some general type in the standard (such as dimensionaltolerance limits), this may be indicated by including thefollowing sentence in the standard:For purposes of determining
26、conformance with these speci-fications, all specified (dimensional tolerance) limits are abso-lute limits, as defined in ASTM Practice E 29, Using Signifi-cant Digits in Test Data to Determine Conformance withSpecifications.5.3.3 If the absolute method is to apply to all specified limitsgiven in a t
27、able, this may be indicated by including a footnotewith the table as follows:CapacitymLVolumetric ToleranceA6 mL10 0.0225 0.0350 0.05100 0.10ATolerance limits specified are absolute limits as defined in ASTM PracticeE 29, for Using Significant Digits in Test Data to Determine Conformance withSpecifi
28、cations.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 significant forpurposes of determining conformance with specifications.6.2 How AppliedWith the rounding metho
29、d, 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 nearestkPa,” “to the nearest 10 ohms,” “to the nearest 0.1 percent,”etc. The rounded value should the
30、n 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 following forms:6.3.1 If the rounding method is to apply to all specifiedlimits in the standard, and if a
31、ll digits expressed in thespecification limit are to be considered significant, this may beindicated by including the following statement in the standard:The following applies to all specified limits in this standard: For purposes ofdetermining conformance with these specifications, an observed valu
32、e or a cal-culated 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 E 29, for Using Significant Digits in Test Data to De-termine Conformance with Specifications.6.3.2 If the ro
33、unding 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 limits for requirements on (tensilestrength), (elongation), and ( . ) given in ., (applicable section
34、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 nearest (1 percent) for (elonga-tion), and to the nearest ( . ) for ( . ) in accor
35、dance with the rounding-offmethod of ASTM Practice E 29 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 in a table, this may be indicated by a note in the mannershown in the following examples:6.3.3.1
36、 Example 1Same significant digits for all items:Chemical Composition,% massCopper 4.5 6 0.5Iron 1.0 maxSilicon 2.5 6 0.5Other constituents (magnesium + zinc + manganese) 0.5 maxAluminum remainderNOTE 4For purposes of determining conformance with these speci-fications, an observed value or a calculat
37、ed value shall be rounded to thenearest 0.1 percent, in accordance with the rounding method of ASTMPractice E 29, for Using Significant Digits in Test Data to DetermineConformance with Specifications.E2906b26.3.3.2 Example 2Significant digits not the same for allitems; similar requirements:Chemical
38、Composition, % massmin maxNickel 57 .Chromium 14 18Manganese . 3Silicon . 0.40Carbon . 0.25Sulfur . 0.03Iron remainderNOTE 5For purposes of determining conformance with these speci-fications, an observed value or a calculated value shall be rounded “to thenearest unit” in the last right-hand signifi
39、cant digit used in expressing thelimiting value, in accordance with the rounding method ofASTM PracticeE 29, Using Significant Digits in Test Data to Determine Conformancewith Specifications.6.3.3.3 Example 3Significant digits not the same for allitems; dissimilar requirements:Tensile RequirementsTe
40、nsile strength, psi 60 000 to 72 000Yield point, min, psi 33 000Elongation in 2 in., min % 22NOTE 6For purposes of determination of conformance with thesespecifications, an observed value or a calculated value shall be rounded offto the nearest 1000 psi for tensile strength and yield point and to th
41、enearest 1 percent for elongation, in accordance with the rounding methodof ASTM Practice E 29 for Using Significant Digits in Test Data toDetermine Conformance with Specifications.6.4 Rounding ProcedureThe actual rounding procedure3shall be as follows:6.4.1 When the digit next beyond the last place
42、 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 the last place to beretained is 5, and there are no
43、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 7This method for rounding 5s is not universally used bysoftwa
44、re 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 areexactlya5ora5followed only by zeros, choose that endingin
45、an even digit. Table 1 gives examples of applying thisrounding-off 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 wo
46、uld 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 specify rounding to thenearest 50, 5, 0.5, 0.05, etc., this may be done by so indicatingin
47、the standard. In order to round to the nearest 50, 5, 0.5, 0.05,etc., double the observed or calculated value, round off to thenearest 100, 10, 1.0, 0.10, etc., in accordance with theprocedure in 6.4, and divide by 2. For example, in rounding6 025 to the nearest 50, 6 025 is doubled giving 12 050 wh
48、ichbecomes 12 000 when rounded to the nearest 100 (6.4.3).When 12 000 is divided by 2, the resulting number, 6 000, isthe rounded value of 6 025. In rounding 6 075 to the nearest 50,6 075 is doubled giving 12 150 which becomes 12 200 whenrounded to the nearest 100 (6.4.3). When 12 200 is divided by2
49、, the resulting number, 6 100, is the rounded value of 6 075.6.7 Special Case, Rounding to the Nearest Interval NotCovered in 6.4 or 6.6In some test methods, there may be arequirement to round a value to an interval that does not alignwith the specific requirements in 6.4 or 6.6, such as to thenearest 0.02, 0.25, 0.3 etc. In such cases, the followingprocedure can be used for rounding to any interval:NOTE 8Using a calculation subroutine that has been programmed toperform the rounding procedure described in 6.7.1, 6.7.2, and 6.7.3 can beadvantageous in evaluati
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