Standard Practice for Using Significant Digits in Test Data ...

1 Designation: E29 13An American National StandardStandard Practice forUsing Significant Digits in Test Data to DetermineConformance with Specifications1 This Standard is issued under the fixed designation E29; the number immediately following the designation indicates the year of originaladoption or, 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 Standard has been approved for use by agencies of the Department of Scope* 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 should aid in clarifying the intended meaning ofspecification limits with which observed values or calculatedtest results are compared in determining conformance This Practice is intended to be used in determiningconformance with specifications when the applicable ASTM specifications or standards make direct reference to this Reference to this Practice is valid only when a choice ofmethod has been indicated, that is, eitherabsolute method orrounding The system of units for this Practice is not speci-fied.

2 Dimensional quantities in the Practice are presented onlyas illustrations of calculation methods. The examples are notbinding on products or test methods 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 safety and health practices and determine the applica-bility of regulatory limitations prior to Referenced standards :2E177 Practice for Use of the Terms Precision and Bias inASTM Test MethodsE456 Terminology Relating 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. TerminologyE456provides a more exten-sive list of terms in E11 value, n the value obtained by making conditions, n conditions 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 Standard deviation (sr), n the standarddeviation of test results obtained under digit any 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 This definition of significant Digits re-lates to how the number is represented as a decimal.

3 It shouldnot be inferred that a measurement value is precise to thenumber of significant Digits used to represent The 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 hastwo significant Digits . Zeros trailing the last nonzero digit fornumbers represented with a decimal point are significant example, the numbers 1270. and 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 haveas few as two or as many as six significant Practice is under the jurisdiction of ASTM CommitteeE11on Quality andStatistics and is the direct responsibility of StatisticalQuality edition approved Aug. 1, 2013.

4 Published August 2013. Originallyapproved in 1940. Last previous edition approved in 2008 as E29 08. referenced ASTM standards , visit the ASTM website, , orcontact ASTM Customer Service at ForAnnual Book of ASTMS tandardsvolume information, refer to the Standard s Document Summary page 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 States1 Provided by IHS under license with ASTM Sold to:NW PA Reg Plann and Dev Co, 849796 Not for Resale,12/05/2014 12:33:37 MSTNo reproduction or networking permitted without license from IHS--``,`,`,```,`,,,,``,``,`,``,,`,-`-`, ,`,,`,`,,` To eliminate ambiguity, the exponen-tial notation may be used. Thus, 105indicates that themodulus is reported to the nearest 105or 1000 Use of appropriate SI prefixes is rec-ommended for metric units to reduce the need for trailing zerosof uncertain significance.

5 Thus, 140 kPa (without the decimalpoint) indicates that the modulus is reported either to thenearest 10 or 1 kPa, which is ambiguous with respect to thenumber of significant Digits . However, MPa clearlyindicates that the modulus is reported to the nearest 1 kPa, MPa clearly indicates that the modulus is reported to thenearest 10 result, n the value of a characteristic obtained bycarrying out a specified test Significance and This Practice describes two commonly accepted meth-ods of rounding data, identified as the Absolute Method and theRounding 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 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 or technologyconcerned, and should therefore be specified in the The unqualified statement of a numerical limit, such as in.

6 Max, cannot, in view of different establishedpractices 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 Method In some fields, specification limitsof in. max, in. max, and in. max are all taken toimply the same absolute limit of exactly two 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 be referred to as theabsolute method, which is discussed in Method In other fields, specification limitsof in. max, in. max, in. max are taken to implythat, for the purposes of determining conformance withspecifications, an observed value or a calculated value shouldbe rounded to the nearest in.

7 , in., in.,respectively, and then compared with the specification will be referred to as therounding method,which isdiscussed in Section7of this Practice gives guidelines for use inrecording, calculating, and reporting the final result for Absolute Applicable The 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 referred to as Applied With 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 Expressed This intent may be expressed in thestandard in one of the following 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, allspecified limits in this Standard are absolute limits, as defined in ASTM PracticeE29, for Using Significant Digits in Test Data to Determine Conformance 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 .

8 For purposes of determining conformance with these specifications, allspecified (dimensional tolerance) limits are absolute limits, as defined in ASTMP ractice E29, for Using Significant Digits in Test Data to Determine Confor-mance with 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 ToleranceA limits specified are absolute limits as defined in Practice E29, for UsingSignificant Digits in Test Data to Determine Conformance with Rounding Applicable The 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 Applied With the rounding method, an observedvalue or a calculated value should be rounded by the procedureprescribed 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 percent, etc.

9 The rounded value should then be compared with thespecified limit, and conformance or nonconformance with thespecification based on this Expressed This intent may be expressed in thestandard in one of the following 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 :E29 132 Provided by IHS under license with ASTM Sold to:NW PA Reg Plann and Dev Co, 849796 Not for Resale,12/05/2014 12:33:37 MSTNo reproduction or networking permitted without license from IHS--``,`,`,```,`,,,,``,``,`,``,,`,-`-`, ,`,,`,`,,`---The following 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 roundingmethod of ASTM Practice E29, for Using Significant Digits in Test Data to De-termine Conformance with 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 limits for requirements on (tensilestrength), (elongation), and (.)

10 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 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 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 1 Same significant Digits for all items:Chemical Composition,% constituents (magnesium + zinc + manganese) maxAluminumremainderFor purposes of determining conformance with these specifications, anobserved value or a calculated value shall be rounded to the nearest , in accordance with the rounding method of ASTM Practice E29 UsingSignificant Digits in Test Data to Determine Conformance with 2 Significant Digits not the same for allitems.