1、Designation: E 29 08An 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 or
2、, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A superscriptepsilon () 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
3、.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 methodswhich
4、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 ASTMspecific
5、ations 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 177 Practice for Use of the Terms Precision and Bias inAS
6、TM Test MethodsE 456 Terminology Relating to Quality and StatisticsE 2282 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: Terminology E 456 provides a more exten-sive list
7、of terms in E11 standards.3.1.1 observed value, nthe value obtained by making anobservation. E 22823.1.2 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
8、within short intervals of time.E 1773.1.3 repeatability standard deviation (sr), nthe standarddeviation of test results obtained under repeatability condi-tions. E 1773.1.4 significant digitany of the figures 0 through 9 that isused with its place value to denote a numerical quantity tosome desired
9、approximation, excepting all leading zeros 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 o
10、f significant digits used to represent it.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 di
11、gits. Zeros trailing the last nonzero digit fornumbers 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 numbersrepresented without use of a decimal point can only beidentified fro
12、m 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. Thus, 1.40 3 105indicates that themodulus is reported to the neare
13、st 0.01 3 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 either to thenearest 10 or 1 kPa, which is ambiguo
14、us with respect to the1This practice is under the jurisdiction of ASTM Committee E11 on Quality andStatistics and is the direct responsibility of Subcommittee E11.30 on StatisticalQuality Control.Current edition approved Oct. 1, 2008. Published October 2008. Originallyapproved in 1940. Last previous
15、 edition approved in 2006 as E 29 06b.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.1*A Summary of Changes
16、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.number of significant digits. However, 0.140 MPa clearlyindicates that the modulus is reported to the nearest 1 kPa, and0.14 MPa clearly indic
17、ates that the modulus is reported to thenearest 10 kPa.3.1.5 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 the
18、Rounding Method. In 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.
19、 Thechoice of method 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
20、 and customs, be regarded 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
21、 2.500 in. max are all taken toimply the same absolute limit of exactly two and a half inchesand for purposes of determining conformance with specifica-tions, an observed value or a calculated value is to be compareddirectly with the specified limit. Thus, any deviation, howeversmall, outside the sp
22、ecification 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 limitsof 2.5 in. max, 2.50 in. max, 2.500 in. max are taken to implythat, for the purposes of determining con
23、formance 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. This will bereferred to as the rounding method ,which is discussed in 6.4.2 Section 7 of this practice giv
24、es 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 digits in an observed value or a calculatedvalue are to be considered significant for purposes of deter-mining
25、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 is not to be rounded, but is to becompared directly with the specified limiting value. Conform-ance or non
26、conformance 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 to all specified limitsin the standard, this may be indicated by including thefollowing sentence in the st
27、andard:For purposes of determining conformance with these specification, all speci-fied limits in this standard are absolute limits, as defined in ASTM Practice E 29,for Using Significant Digits in Test Data to Determine Conformance with Specifi-cations.5.3.2 If the absolute method is to apply to al
28、l 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 conformance with these specifications, allspecified (dimensional tolerance) limits are absolute limits, a
29、s defined in ASTMPractice E 29, for Using Significant Digits in Test Data to Determine Conform-ance 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 Tolera
30、nceA6 mL10 0.0225 0.0350 0.05100 0.10ATolerance limits specified are absolute limits as defined in Practice E 29, forUsing Significant Digits in Test Data to Determine Conformance with Specifica-tions.6. Rounding Method6.1 Where ApplicableThe rounding method applies whereit is the intent that a limi
31、ted 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 method, an observedvalue or a calculated value should be rounded by the procedureprescribed in 4.1.3 to the near
32、est 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 then be compared with thespecified limit, and conformance or nonconformance with thespecification based on thi
33、s 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 all digits expressed in thespecification limit are to be considered significant, this may beindicated by inc
34、luding 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 value or a cal-culated value shall be rounded “to the nearest unit” in the last right-hand digitused in express
35、ing 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 rounding method is to apply only to the specifiedlimits for certain selected requirements, this may be indica
36、tedby including the following statement in the standard:E29082The following 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 specif
37、ications, 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 accordance with the rounding methodof ASTM Practice E 29 Using Significant Digits in Test Data to Determin
38、e Con-formance 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 Example 1Same significant digits for all items:Chemical Composition,% massCopper 4.5 6 0.5Iron 1.0 maxSi
39、licon 2.5 6 0.5Other constituents (magnesium + zinc + manganese) 0.5 maxAluminum remainderFor purposes of determining conformance with these specifications, anobserved value or a calculated value shall be rounded to the nearest 0.1 per-cent, in accordance with the rounding method of ASTM Practice E
40、29 UsingSignificant Digits in Test Data to Determine Conformance with Specifications.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
41、purposes of determining conformance with these specifications, anobserved value or a calculated value shall be rounded “to the nearest unit” inthe last right-hand significant digit used in expressing the limiting value, in ac-cordance with the rounding method of ASTM Practice E 29 Using SignificantD
42、igits in Test Data to Determine Conformance with Specifications.6.3.3.3 Example 3Significant 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 c
43、onformance with these specifications, anobserved value or a calculated value shall 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 E 29 Using Signifi-cant Digits in Test Data to
44、 Determine Conformance with Specifications.6.4 Rounding ProcedureThe actual rounding 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 ber
45、etained 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 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 eve
46、n. 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 sign
47、ificant digits, choose that which is nearest. Iftwo choices are possible, as when the digits dropped areexactlya5ora5followed 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 rou
48、nding 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
49、 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 the standard. In order to round to the nearest 50, 5, 0.5, 0.05,etc., double the observed or calculated value, round 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 whichbecomes 12 000 when rounded to the nearest 100 (6.4.3).When 12 000 is divided by 2, the resulting number, 6 0
