1、Designation: D 6026 06Standard Practice forUsing Significant Digits in Geotechnical Data1This standard is issued under the fixed designation D 6026; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A numbe
2、r in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.1. Scope*1.1 This practice is intended to promote uniformity inrecording significant digits for measured and calculated valuesinvolving geotechnical da
3、ta. The guidelines presented areindustry standard, and are representative of the significantdigits that should generally be retained. The guidelines do notconsider material variation, purpose for obtaining the data,special purpose studies, or any considerations for the usersobjectives; and it is com
4、mon practice to increase or reducesignificant digits of reported data to be commensurate withthese considerations. It is beyond the scope of this practice toconsider significant digits used in analysis methods for engi-neering design1.1.1 Using significant digits in geotechnical data involvesthe pro
5、cesses of collecting, calculating, and recording eithermeasured values or calculated values (results), or both.1.2 This practice accepts a variation of the traditionalrounding method that recognizes the algorithm common tomost hand-held calculators, see 5.2.3. The traditional roundingmethod (see 5.2
6、) is in accordance with Practice E29 orIEEE/ASTM SI 10.1.3 This practice offers a set of instructions for performingone or more specific operations. This document cannot replaceeducation or experience and should be used in conjunctionwith professional judgment. Not all aspects of this practice maybe
7、 applicable in all circumstances. This ASTM standard is notintended to represent or replace the standard of care by whichthe adequacy of a given professional service must be judged,nor should this document be applied without consideration ofa projects many unique aspects. The word “Standard” in thet
8、itle of this document means only that the document has beenapproved through the ASTM consensus process.2. Referenced Documents2.1 ASTM Standards:2D 653 Terminology Relating to Soil, Rock, and ContainedFluidsD 2905 Practice for Statements on Number of Specimensfor TextilesD 4356 Practice for Establis
9、hing Consistent Test MethodTolerancesD 6913 Test Methods for Particle-Size Distribution (Grada-tion) of Soils Using Sieve AnalysisE29 Practice for Using Significant Digits in Test Data toDetermine Conformance with SpecificationsE 344 Terminology Relating to Thermometry and Hydrom-etryE 456 Terminolo
10、gy Relating to Quality and StatisticsE 833 Terminology of Building EconomicsIEEE/ASTM SI 10 Standard for Use of the InternationalSystem of Units (SI): The Modern Metric System3. Terminology3.1 Definitions:3.1.1 For common definitions of soil and rock terms in thisstandard, refer to Terminology D 653
11、.3.1.2 accuracy, nthe degree of agreement of an individualmeasurement or average of measurements with an acceptedreference value, or level. See Terminology E344-973.1.3 calculated value, nthe resulting value determinedby processing measured value(s) using an equation. SeePractice D 4356 - 84(Reappro
12、ved 1996).3.1.3.1 DiscussionIn many cases the calculated value(s)is considered a determination value(s).3.1.4 determination value, nthe numerical quantity calcu-lated by means of the test method equation from the measure-ment values obtained as directed in a test method. See PracticeD 4356 - 84(Reap
13、proved 1996).3.1.5 measurement value, nthe resulting value determinedby measuring a dimension, quantity, or property.3.1.5.1 DiscussionIn many cases the term “measuredvalue(s)” is also referred to as “measurement value(s)”. SeePractice D 4356 - 84(Reapproved 1996).3.1.6 precision, nthe closeness of
14、agreement betweenindependent test results obtained under stipulated conditions.See Terminology E 456 - 96.3.1.6.1 DiscussionPrecision depends on random errorsand does not relate to the true or specified value.1This practice is under the jurisdiction of ASTM Committee D18 on Soil andRock and is the d
15、irect responsibility of Subcommittee D18.91 on StandardsDevelopment and Review.Current edition approved Nov. 1, 2006. Published December 2006. Originallyapproved in 1996. Last previous edition approved in 2001 as D 602601e1.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcont
16、act 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 section appears at the end of this standard.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West
17、 Conshohocken, PA 19428-2959, United States.3.1.6.2 DiscussionThe measure of precision usually isexpressed in terms of imprecision and computed as a standarddeviation of the test results. Less precision is reflected by alarger standard deviation.3.1.6.3 Discussion“Independent test results” means re-
18、sults obtained in a manner not influenced by any previousresult on the same or similar test object. Quantitative measuresof precision depend critically on the stipulated conditions.Repeatability and reproducibility conditions are particular setsof extreme conditions.3.1.7 rounding, nthe process of r
19、educing the number ofdigits in a number according to rules relating to the requiredaccuracy of the value.3.1.8 significant digitany of the integers one through nineand zeros except leading zeros and some trailing zeros.3.1.8.1 Zero is a significant digit if it comes between twonon-zero integers.3.1.
20、8.2 Zeros leading the first nonzero digit of a numberindicate the order of magnitude only and are not significantdigits. For example, the number 0.0034 has two significantdigits.3.1.8.3 Zeros trailing the last nonzero digit for numbersrepresented with a decimal point are significant digits. Forexamp
21、le, 4.00 and 4.01 have three significant digits.3.1.8.4 The significance of trailing zeros for numbers rep-resented without use of a decimal point can only be identifiedfrom knowledge of the source of the value.3.1.9 test result, nthe value obtained by applying a giventest method, expressed as a sin
22、gle determination or a specifiedcombination of a number of determinations. See PracticeD 2905 - 91.3.2 Definitions of Terms Specific to This Standard:3.2.1 sensitivity analysis, na test of the outcome of ananalysis by altering one or more parameters from an initiallyassumed value(s). See Terminology
23、 E 833 - 97b.3.2.1.1 DiscussionSensitivity analyses are often related tothe design process, but not exactly applied in that designprocess. A sensitivity analysis might include how measuredshear strength or hydraulic conductivity varies with moldingwater content and percent compaction.3.2.2 variabili
24、ty analysis, nthe determination of the varia-tion in values within a given boundary condition(s)3.2.2.1 DiscussionA variability analysis might includehow a given property varies with depth.4. Significance and Use4.1 The guidelines presented in this practice for retainingsignificant digits and roundi
25、ng numbers may be adopted by theusing agency or user. Generally, their adoption should be usedfor calculating and recording data when specified requirementsare not included in a standard.4.2 The guidelines presented herein should not be inter-preted as absolute rules but as guides to calculate and r
26、eportobserved or test data without exaggerating or degrading theaccuracy of the values.4.2.1 The guidelines presented emphasize recording data toenough significant digits or number of decimal places to allowsensitivity and variability analyses to be performed, see 3.2.5. Guidelines for Rounding Numb
27、ers in Calculating andRecording Data5.1 General DiscussionRounding data avoids the mis-leading impression of precision while preventing the loss ofinformation due to coarse resolution.Any approach to retentionof significant digits of necessity involves some loss of infor-mation; therefore, the level
28、 of rounding should be selectedcarefully considering both planned and potential uses for thedata. See Practice E29.5.2 Rounding NumbersWhen a numerical value is to berounded to fewer digits than the total number available, use thefollowing procedure which is in accordance with Practice E29or IEEE/AS
29、TM SI 10:When the first digitbeyond the last placeto be retained is:The digit in the lastplace retained is: Examples5 increased by 1 2.464 to 2.5Exactly 5 increased by 1 2.55 to 2.6if it is odd orunchanged if it is even 2.45 to 2.45 followed only same as above 2.5500 to 2.6by zeros for exactly 5 or2
30、.4500 to 2.45.2.1 The rounded value should be obtained in one step bydirect rounding of the most precise value available and not intwo or more successive rounding steps. For example, 89 490rounded to the nearest 1000 is at once 89 000. It would beincorrect to round first to the nearest 100, giving 8
31、9 500 andthen to the nearest 1000, giving 90 000.5.2.2 The same rule applies when rounding a number withmany digits to a number with a few digits as occurs when usinga computer or calculator that displays the answer to a compu-tation as ten or more digits and the answer is to be recorded toa few dig
32、its. For example, the number 2.34567 rounded to twosignificant digits would be 2.3.5.2.3 Calculators and computers, in general, do not followall the rules given in 5.2, (that is, only rounding up odd digitsfollowed by a five, while even digits stay the same (2.55 to 2.6or 2.45 to 2.4) and generally
33、always round up. Recognizingthe widespread use of calculators and computers that alwaysround up, their use shall not be regarded as nonconformingwith this practice.5.2.4 The numbers to be reported are rounded at the end ofcalculations to the appropriate number of significant digits, notprior to the
34、calculations (See section 5.4.5.3 Recording Measured DataWhen recording measuredvalues, as in reading marks on a burette, ruler, or dial, recordall digits known exactly, plus one digit, which may beuncertain due to estimation.5.3.1 When the measuring device has a vernier scale, recordthe last digit
35、from the vernier.5.3.2 The number of significant digits given by a digitaldisplay or printout from an instrument should be greater than orequal to the sensor to which it is connected. Care should betaken not to record digits beyond the precision of the sensor,however. For example, using a pressure t
36、ransducer with theD6026062precision of 1 kPa should not be read to the nearest 0.1 kPabecause the readability of the output instrument displays moredigits.5.4 Calculation of Measured DataWhen using measuredvalues to produce a calculated value(s), avoid rounding ofintermediate quantities. As far as p
37、racticable with the calcula-tion device or data sheet/form used, or both, carry outcalculations exactly as they occur (no reduced digits) andround the final value/result.5.5 Recording DataThe recorded data should conform toinstructions in the respective standards. For example, thecomputed water cont
38、ent values used in determining the liquidand plastic limits of a soil are recorded on the data sheet/formto the nearest 0.1 %, see Table A1.1. While the liquid andplastic limits are recorded, reported, or summarized to thenearest whole number and the percent designation is omitted.5.5.1 If the numbe
39、r of significant digits or number ofdecimal places in the measured and calculated value(s) is notspecified in the respective standard, then one may use thefollowing approach. Use Table A1.1 to determine the numberof significant digits or number of significant digits or numberof decimal places in the
40、 calculated value(s). Using that value(s)and the rules of significant digits as described in Section 6,determine the required significant digits or number of decimalplaces for the measured value(s).5.5.2 If a standard has a conflict between the measured andcalculated value(s) related to significant
41、digits or number ofdecimal places, then use the following criterion. The criterionspecified for calculated value(s) should govern how the mea-sured value(s) is determined and recorded.6. Guidelines for Retaining Significant Digits inCalculating and Recording Data6.1 Upon completion of mathematical c
42、alculations, use thefollowing rules as guidelines to determine the proper numberof significant digits or decimal places of rounded numbers.6.1.1 The rule when multiplying or dividing is that the resultshall contain no more significant digits than the value with thesmaller number of significant digit
43、s. Examples include:6.1.1.1 11.38 3 4.3 = 49, since the factor 4.3 has two sig-nificant digits.6.1.1.2 Determine the volume, V, of an object having a basearea, A, of 28.48 in.2and a height, h, of 6.12 in., V = Ah= (28.48 in.2) (6.12 in.) = 174, the answer to three significantfigures in agreement wit
44、h the height measurement.6.1.2 The rule when adding or subtracting data is that thenumber of decimal places in the result is the same as in thenumber containing the fewest digits following the decimal.Examples include:6.1.2.1 11.24 + 9.3 + 6.32 = 26.9, since the last significantdigit of 9.3 is the f
45、irst following the decimal place, and 26.9results by rounding the exact sum, 26.86.6.1.2.2 (926 923.4) = 3.6.1.2.3 (926 923.4) x 11.38 x 4.68/2.00 = 70, not 69 or69.2 since there is only one significant digit in the difference.This means, although there is a minimum of three significantdigits in the
46、 input values, you could only record or expect tocheck the result to one significant digit. This is an importantfactor to consider when recording and checking a calculatedvalue(s) that include a difference(s), see Note 1.NOTE 1Typical examples of calculated values which include adifference(s) are wa
47、ter content, void ratio, deformation, degree of satura-tion, and specific gravity.6.1.3 The rules for logarithms and exponentials are: digitsof ln(x)orlog10( x) are significant through the nth place afterthe decimal when x has n significant digits. The number ofsignificant digits of exor 10xis equal
48、 to the place of the lastsignificant digit in x after the decimal. Examples include:6.1.3.1 ln(3.46) = 1.241 to three places after the decimal,since 3.46 has three significant digits.6.1.3.2 103.46= 2,900 has two significant digits, since 3.46is given to two places after the decimal.6.1.4 When an ex
49、act count is used in a calculation with anumber, the number of significant digits in the result is thesame as the number of significant digits in the number. Forexample, the sum of two measurements was found to be 8.24in. To find the average value, this sum must be divided by two.In this case, however, two is not a measurement but an exactcount. Therefore, 8.24 in./2 = 4.12 in. Since 8.24 has threesignificant digits, the results also contain three significantdigits.6.1.5 To preserve accuracy in calculations using constants,or conversion factors with measur
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